My agitator is not working in my washer- it is a kenmore elite. the agitator seems locked up. Everything else works fine.

The agitator is driven by a couple of different methods. The first is the agitator is splined and slips onto the matching splines of the agitator shaft from the transmission. The second is the use of a bell coupling which is splined to the agitator shaft as well and the agitator snaps onto the coupling. If the agitator does not agitate, first remove the agitator and watch the agitator shaft to see if it is working properly. This will require a small load setting of water and the machine set to run. If the agitator shaft is working properly, it is either the splines on the agitator or the bell coupling that is defective. If the agitator shaft does not work properly, the problem is in the transmission.
Hope this helps.