We have used numerical methods to solve the Kohn-Sham equations of the Density Functional Theory DFT, within local density approximation LDA employing different pseudopotentials in order to obtain equilibrium structure and properties of some materials (namely Si, Cu, and Ni). We used in these calculations a number of pseudopotentials in order to obtain the most accurate results, and we varied the computational procedure by choosing different Kpoint sampling and different numerical methods for the same purpose. The results we have obtained from these ab initio calculations are in good agreement with experimental results, which allows us to use the same techniques for further study of some properties of materials.