My 2001 Buick LeSabre Custom cuts out upon start up when applying the gas pedal. Also under acceleration, especially until it's warmed up. But will do it under every acceleration even at highway speeds and I accelerate to pass or change lanes.

SOURCE: My Sister's 1994 Buick LeSabre revs up upon start

I had the same problem on my 1994 Buick Regal Custom, I replaced the mass air flow sensor. Now i have no problems.

SOURCE: 2001 Ford F650 with 7.2 Cat deisel acceleration problem

Check your TPS Throttle positioning sensor. Sounds like it has a dead spot in it or it is failing. May also be a wiring harness issue or loose connection at TPS too! If its intermittent then it will soon go out completely. It should be located on your fuel pedal. Remove it and check it with an ohm meter. Check resistance all the way thru from 0-100 percent. When it is not working it should do nothing and show no resistance. When it is working the resistance value will increase and or decrease as you turn the sensor.

SOURCE: 2001 Buick Lesabre makes a whining/humming noise

whinning while in park