In order to achieve the required high level of mechanical material components as regards sustainability and safety, the stiffness of such materials has to be thoroughly investigated to avoid failure. This study investigates, analytically, the stiffness of some mechanical materials with different cross-sectional areas, whose mechanical properties are homogeneous and isotropic. The exerted force for steel material solids with different cross-sections was investigated. Comparisons were made and results are consistent with the ones in literature. A computer software, Maple, was used to plot the three-dimensional graphs of the relationship between the parameters. Specifically, it was observed that the steel hollow rectangular beam cross-section has a high axial stiffness compared to that of steel hollow circular beam cross-section. Also, the moment of inertia of the steel beams, considered, depend on their cross-sectional areas.