The work presented consists on the one hand of researching the values of the stresses and displacements of a plate subjected to a perpendicular external force, the distribution of the stress is determined at the end of the localization of the maximum stress. On the other hand, verified that the natural frequency is the excitation frequency, so as not to have a resonance. The equilibrium equations are obtained by applying the principle of virtual work. The mathematical expressions of displacements, normal and tangential stresses are obtained by using the Navier approach to solve the equilibrium equation system. The stiffness matrix and mass matrix are calculated by exact integrations based on the finite element method. The results obtained agree well with those given in the bibliography and those obtained by using the ANSYS apdl code for the calculation of finite elements. Key words: finite elements, stress, displacement, force, a plate, frequency, resonance.