Abstract <p>The problem of three-dimensional numerical modeling electrophysics problems related to the generation of high-current relativistic electron beams (REB) is considered. The relevance of the problem physical formulation is due to the need to develop perspective microwave devices for a wide range of applications. The paper discusses nonlinear wave processes in a magnetically insulated microwave generator that generate REB. A special feature of the mathematical problem formulation is the real three-dimensional geometry of the generator. The mathematical model is based on the complete system of Maxwell’s equations, supplemented by the equations of motion for relativistic charged particles. The birth of these particles is caused by the processes of field emission and the formation of relativistic plasma. A new numerical method for solving a spatially three-dimensional problem is proposed. It combines explicit time schemes, the finite volume method on irregular grids, and the cloud particle method. The developed numerical method on special-type grids has a second-order approximation and accuracy on spatial and temporal variables. The software implementation of the method is initially focused on parallel computing. To test the method, a number of actual problem statements with different geometric parameters are considered. The analysis of the numerical results confirmed the reproduction in the developed three-dimensional code of one-dimensional and two-dimensional solutions.</p>