I have a Kenmore Elite top load washer, model # 110.16972500. I got a shoelace cought under the agitator.

Hi and welcome to FixYa, I am Kelly

Take a look at this link so you can see what parts secure your agitator in place:
http://www.searspartsdirect.com/partsdirect/partsdirect/showSubComp.pd?imageUrl=http%3a%2f%2fc.searspartsdirect.com%2flis_png%2fPLDM%2fK0507016-00003.png

Also see this link for item number descriptions:
http://www.searspartsdirect.com/partsdirect/part-model/Kenmore-elite-Parts/Washer-Parts/Model-11016972500/0583/0153200/K0507016/00003?blt=06&prst=0&shdMod=11016972500

You have to lift off the cap (Item 1) and then the inner cap & washer (Items 22 and 23) to get to the mounting bolt item 21. You will have to use a socket and an extension to remove the agitator mouting bolt. After removing the mounting bolt you should be able to lift the agitator to free the shoe lace. Re-assemble in reverse order. Mounting bolt... inner cap and washer... then the top cap.

Thanks for choosing FixYa,
Kelly