This work deals with the modal superposition technique developed to obtain the solution of the dinamic equilibrium equations resulting from the finite element space discretization method. For that numerical solution the eigenpair solution associated to the eigenvector problem arisen from the vibration characteristics of undamped discretized structures. It is proposed an algorithm where the eigensolution is obtained combining the Lanczos and the QR methods. This solution, through base of definition transformation, is used to decouple the dinamic equilibrium equations with the modal superposition method. The analises presented in this work were developed considering systems without damping. However, analytical solution for systems with damping are also presented. The algorithm was implemented in the computer and some numerical results are compared to the other analytical and/or numerical solution to identify its performance and applicability in the solution of dynamic systems.