Andrew,

I presume that you can first calculate the force between two fingers by
evaluating the Maxwell stress on either of the beam.  Then it becomes a "simple"
problem for bending of one beam anchored on one side under stress.  Searching
for any handbook for beam bending, you should be able to find the equation and
solutions of the deflection (which I presume you are interested in) of the beam.

Ning Wu
The Department of Chemical Engineering
Princeton University
New Jersey 08544