A Numerical Analyzer for Scientific and Industrial Requirements (NASIR) software which utilizes novel matrix free Finite Volume is applied for solving plane strain solid state problems on linear triangular element meshes. The developed shape function free Galerkin Finite Volume structural solver explicitly computes stresses and displacements in Cartezian coordinate directions for the two dimensional solid mechanic problems under either static or dynamic loads. The accuracy of the introduced algorithm is assessed by comparison of computed results of cantilever structural elements under static concentrated load with analytical solutions. Then, the performance of the introduced method to solve structural plane strain problem under forced and vibrating loads is demonstrated. The performance of the solver is presented in terms of stress and strain contours as well as convergence behavior of the method
