2000 elantra. I have to first put the transmition In drive then back to reverse to get reverse to engauge? Also the car will not goto overdrive. It has 118000 miles on it.

Do you have a check engine light on? Any fault codes?

Well I would guess there is a solenoid internally in the transmission that fails intermittently go to a local transmission shop make sure it's reputable have them test drive your car and u can ride with they will hook up a computer which will read all of the functions of the transmission that will b the best and cheapest way to exactly figure out you problem thanx Chris

Check motor mounts, check CV joints both of thees issues can cause the engine to stutter or shake the other possibility is a fault in the overdrive system of the transmit ion
if you have overdrive . also engin idle should be about 500 to 700 rpm normal any higher will case an abruptness .

check the oil level by applying handbrake then start engine and put in reverse ,then check oil level if oil level ok have a drive around dealers and trade it in quick before you have to pay out for a new gearbox

sounds like its internal, like the reverse band, that applies the overdrive, or the clutches that apply when in overdrive, either way the reverse band and overdrive clutches work hand in hand, for overdrive and reverse... id say you need a rebuild or a junk yard unit.... :( sorry for the bad news.

My advice is to weigh the asking price for the car against a transmission repair. Incidentally, it is not necessarily debilitating for the overdrive not to work but it will eventually lead to a transmission overhaul or replacement which is costly.

pull the shifter back slowly out of park and see if it engauges before or after the reverse position this could just need an adjustment in the cable if not it's an 08 you probably still have a warranty on it i would take it to the dealer if no warranty ammco or any othyer transmission shop can run a few tests on it for a low fee

4R100 or 4R70W?

Geartrain
Power is transmitted from the torque converter to the geartrain components through the input shaft and forward clutch cylinder.

• By holding or driving certain members of the gearset, four forward ratios and one reverse ratio are obtained and transmitted to the output shaft. The ratios are as follows:

GEAR RATIO 1ST 2.71 to 1 2ND 1.54 to 1 3RD 1.00 to 1 4TH 0.71 to 1 REVERSE 2.18 to 1
Input Shaft
The input shaft is supported by two bushings in the stator support. End positioning of the input shaft is controlled by the splines in the converter turbine and the overdrive planet assembly.
Output Shaft
The output shaft is supported by two bushings in the case and by the slip-yoke and bushing in the extension housing. End positioning is controlled by the parking pawl gear and snap ring or shoulder and by the reverse ring gear hub and snap ring.
Overdrive System
The overdrive planetary system consists of the overdrive planet assembly, overdrive sun gear, overdrive ring gear, coast clutch cylinder, overdrive one-way clutch assembly and the center shaft, as shown in the following illustration. The overdrive planet assembly is splined to the input shaft. The overdrive sun gear is centered by a bushing on the input shaft and held in place laterally by needle bearings on the reactor support and the overdrive planet assembly. The overdrive sun gear is splined to the coast clutch cylinder, which in turn is splined to the overdrive one-way clutch inner race.
The outer race of the one-way clutch is splined to the overdrive ring gear, which is splined to the center shaft. The center shaft is centered by the forward planetary assembly and is laterally held by needle bearings on the center support and the overdrive planet assembly. The center shaft is splined into the forward clutch cylinder.
Two friction clutches are assembled in the overdrive planet assembly. The coast clutch is splined between the coast clutch cylinder and the overdrive ring gear. The coast clutch is activated to perform engine braking in MANUAL 1, MANUAL 2 and third gear with the transmission control switch engaged.
The overdrive clutch is splined between the case and the coast clutch cylinder. The overdrive clutch holds the coast clutch cylinder and, in turn, the overdrive sun gear, to permit the planet assembly to overdrive the ring gear.
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Forward Drive System
The forward drive system consists of the forward clutch cylinder, intermediate brake drum, intermediate one-way clutch, input shell, forward ring gear, forward ring gear hub, forward/reverse sun gear and the forward planetary carrier and forward planetary gears.
The forward clutch cylinder is splined on the center shaft. The forward ring gear is piloted on the forward ring gear hub. Thrust bearings on the forward planet assembly and forward clutch cylinder hold the forward ring gear hub in place.
The intermediate brake drum is radially supported by bushings on the center support and is laterally controlled by thrust washers on the forward clutch cylinder and center support. The intermediate brake drum has the inner race of the intermediate one-way clutch press-fitted on its pilot. The intermediate one-way clutch's outer race is splined to the intermediate friction clutch, which is splined to the case. The intermediate brake drum has lugs that are slotted into the input shell to form a mechanical connection. The input shell is splined into the forward/reverse sun gear. The forward/reverse sun gear is common to two planetary gearsets. The forward planet is splined to the output shaft and is laterally positioned by needle bearings on the sun gear and on the forward clutch cylinder, as shown in the following illustration.
Two friction clutch assemblies, the direct clutch and the forward clutch, are shown with the forward planetary assembly. The direct clutch assembly splines the forward clutch cylinder to the intermediate brake drum. The forward clutch assembly splines the forward clutch cylinder to the forward ring gear. The forward clutch is activated during all forward gears. While in third or fourth gear, both the direct and forward clutches are applied to hold the forward planetary assembly and enable it to act as a solid shaft.
In second gear, the intermediate clutch assembly holds the forward/reverse sun gears. It is applied, along with the intermediate one-way clutch, to hold the intermediate brake drum, input shell and forward/reverse sun gear. In higher gears, the one-way clutch overruns.
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Low and Reverse Drive System
The reverse planetary assembly consists of the reverse planetary carrier, reverse planet gears, the reverse ring gear, the reverse ring gear hub, the reverse clutch hub and the low-reverse one-way clutch assembly.
The reverse ring gear hub is splined to the output shaft and to the reverse ring gear. The reverse ring gear hub is laterally held by a needle bearing on the inner race of the low-reverse one-way clutch and a snap ring on the output shaft. The reverse planet assembly is splined to the low-reverse clutch hub. The low-reverse clutch hub is connected by the reverse clutch to the case. The inner race of the one-way clutch is bolted to the case.
The reverse clutch assembly is activated in REVERSE gear and in MANUAL 1. The reverse clutch bypasses the reverse one-way clutch during coast and MANUAL 1. The reverse clutch holds the reverse planet assembly in REVERSE gear to enable the sun gear to drive the reverse ring gear in the opposite direction.
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Apply Components
The following information describes the operation of the three 4R100 one-way clutches.
One-Way Clutch—Overdrive
The overdrive one-way clutch, shown in the following illustration, transmits engine torque from the overdrive sun gear to the overdrive ring gear in first, second and third gear range. The overdrive one-way clutch transmits power when the sprags are engaged between the inner and outer races. The inner race is splined to the coast clutch cylinder, which in turn is splined to the overdrive sun gear. The outer race is splined to the overdrive ring gear.
The overdrive one-way clutch engages whenever the overdrive planetary system attempts to drive the overdrive sun gear clockwise when the overdrive ring gear has a counterclockwise torque from the vehicle. When torqued counterclockwise, the overdrive one-way clutch engages and acts as a wedge to lock the sun gear and the ring gear together. During coast, the overdrive one-way clutch enables the ring gear to overrun or spin at a faster rate than the sun gear.
The overdrive one-way clutch overruns when in overdrive (fourth gear). In overdrive, the coast clutch cylinder is held by the overdrive one-way clutch, which in turn holds the overdrive sun gear. This causes the overdrive planet assembly to walk around the sun gear and overdrive the overdrive ring gear. The inner race of the overdrive one-way clutch is thus held stationary while the outer race is allowed to overrun clockwise.
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could be 1 of 2 things the overdrive button isnt working or the overdrive solinoid on the gear box isnt working

Check you transmission fluid level and if it's not your transmission, I'm thinking that your brake shoe lineing in the rear brakes may have separated and is jamming up aginst the drums when your trying to back up. Sorry can't halp you with any more, good luck and start with that and hope it help's.