The article discusses a multi-axis electromagnetic vibration stand (EMVS), in which oscillations of the platform are excited, connected in a certain way with three armatures, and an alternating magnetic field acts on the armatures. For rational design and subsequent analysis of the properties of EMVS on the basis of the apparatus of analytical mechanics, a correct mathematical model has been developed, which contains the differential equations of mechanical motion, as well as the equations of electromagnetic processes. Electromagnetic and mechanical quantities that characterize the movement of systems appear as formally equal. The mathematical model includes a system of nine differential equations with the same number of unknowns. Considering the complexity of the resulting system, its further research was carried out using computer technology. As a result, the dependences of the linear and angular coordinates and velocities, as well as the current strength in time, were obtained. The corresponding graphs have been built. Also built phase portraits for linear and angular parameters. The resulting mathematical model takes into account the features of the nonlinearity of the system. Under certain conditions, chaotic behavior of the system is possible. The calculation formulas obtained in the process of mathematical modeling and presented in this article, as well as the program created and implemented on a computer, make it possible to analyze the influence of all EMVS parameters both separately and in their relationship on the characteristics of the system. In addition, the obtained formulas provide the possibility of designing EMVS with the most rational characteristics and the optimal ratio of design parameters. The obtained mathematical model of EMVS is the basis for mathematical modeling when testing vibration stands, as well as for the analysis and synthesis of control systems with feedback on acceleration, force, product of force and acceleration.