Our project consists of two parts (A and B). In part A we solve a linear elasticity problem with implementing a rotated  approximation method and simulating the problem in commercial softwares (COMSOL and SolidWorks). To evaluate the results we implement an analytical eigenvalue solver. As a simple case, we use a cube with side length of L = 1m made of Alloy steel with density of 7850 Kg/m^3.  In part B we implement a time dependent linear elasticity problem on a beam made of Alloy steel with density of 7850 Kg/m^3 with size of 1x0.1x0.01m. We use the implicit method to solve our problem. The frequency results in part A show that the rotated Q1 approximation method works more accurate than the commercial software.