The drive with articulated joints is an evolutionary dynamical system. Modal and spectral properties of the relative lateral vibration in a rotating space are dependent on the angular velocity of the shaft rotation. This problem can be the first solved analytically. More complex systems can be solved either by discretization using the finite element method and converting it to eigenvalues, eigenvectors, or using the transfer-matrix method, which is a combination of analytical solutions and numerical methods. The article is derived a finite element for the one-dimensional linear continuum in the state of combined bending-gyratory vibration. Furthermore, the applicaton of the finite element method designed and tuned a method for calculating eigenvalues and vectors of a stepped shaft in the state of combined bending-gyratory vibration. It is made a comparison of the mentioned methods.