Rami 
December 5, 2012 06:09 
Hi Hooman,
The equations used in stress analysis for solids are nearly identical to those of the momentum equations for viscous fluid flow, except that for solids stands for the displacement vector, whereas for fluids  it is the velocity (the stress is related to strain for solid and to strainrate in fluids).
You should also choose whether you use an Eulerian or Lagrangian formulation. The Lagrangian formulation in Cartesian coordinates is simply (using tensor notation where D/Dt is the material derivative, comma is the covariant derivative  which degenerates to simple spatial derivative in Cartesian coordinates, is the displacement, is the stress, is the body force and is the density).
If you treat small displacement and small strain, the various stress and strain measures (Cauchy, PiolaKirchhoff, Green, Lagrange, etc.) are identical and their relation to each other are practically the same as those for fluids, e.g. for elasticity , where and are the Lame modulii and .
Nevertheless, I still suggest to look into FEM, which has much more literature on solids. It is in many ways similar (and more consistent and general) to FVM. Actually, FVM can be viewed as a special case of FEM, using piecewiseconstant shapefunctions and some additional minor approximations.
