In order to solve the current situation of multi-span stepped beam without simple analytical form of natural frequency equation, an analytical model of closed solution for free vibration of multi-span stepped beams is established in this paper. Firstly, based on the EulerBernoulli beam theory, the frequency equation of a single span beam with elastic boundaries is calculated, which composed of trigonometric functions and hyperbolic trigonometric functions. And also the four parameters of transverse spring stiffness and rotational spring stiffness are included in the obtained frequency equation. The beam’s frequency equations for six cases of different boundary conditions including at least one kind of spring stiffness are presented in table form. Then a free vibration analysis model for multi-span beam is established, in which the multi-span beam with stepped sections is equivalent to the superposition of vibration of split beam segments with elastic boundary. Combined with the dynamic equilibrium equation presented by the infinitesimal section located at the linked node between beam segments, the closed-form expressions for natural frequency of multi-span stepped beam are obtained. For several cases of multi-span beam with different boundaries or internal supports,the first several natural frequencies and mode shapes are obtained in the numerical examples. The frequency characteristic equation of a stepped multi-span beam and a uniform-section multi-span beam can be unified in the same form. Compared with the results by using the finite element simulation, the relative deviation is less than 1%, which indicates that the proposed method is reasonable and effective. The natural vibration frequency of a multi-span stepped beam varies with the position, radius and moment of inertia of the supporting bar. The analytical frequency equation is theoretically accurate with a brief form, which has good potential application value and can be used to validate the precision of other numerical methods.