Here's a little example I whipped up...

http://uk.youtube.com/watch?v=Qr3uhKokS5o

This was done using a bend deformer on a small poly plane with another larger plane next to it and below it.
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In maya you don't really animate the individual vertices for something like this, you can animate vertices using deformers like the 'lattice' or making 'blendshapes'.

For the example you gave with...