In this paper, a Trujillo algorithm method for the exact solution of nonlinear explicit dynamic problems is developed. This method associates numerical techniques and it is applied to determine the natural frequencies of structures. The numerical predictions of the natural frequency are compared to analytical and experimental results. There was no direct method available for solving such a problem efficiently in the case of explicit dynamic analysis. The Trujillo algorithm is an indirect method and the approach is based upon the principle of conservation of energy. It is believed that the proposed method provides a powerful engineering tool in the analyzing of structures.