Abstract: The subject of our study is to apply the mixed finite element for solving the Navier-Lame system with a new boundary condition. We compare between mini-element method and the ordinary finite element by the other side. We calculate the displacement and its divergence simultaneously by using an extra unknown. We propose a new method of comparison, we calculate the rate " that is called a speed of convergence found by each of the both numerical methods, all this will be done by using the linear regression. An analytical example is used to validate the accuracy, convergence and robustness of the present mixed finite elements method for elasticity.