The paper describes a three-dimensional computer model and a desktop program in the Visual C++ platform, which is intended to provide a reference simulation of the dynamics of a wedge-shaped electron beam in a cylindrical triode type accelerating device. Such a triode-type source of intense radial converging beam is employed in improving the material surface properties of a specimen used as an anode. The simulation model has been developed with the highest possible generality and adequacy achievable under the given computing environment and limitations that do allow using it for the validation and benchmarking. The software package covers the calculation of the electrostatic field by the difference method on a cubic grid, the calculation of the beam own field using the ”particle–particle” (PP) method, the calculation of the trajectories of the motion of macro particles using Runge–Kutta solvers of the 4th order (taken as the reference) and lower orders. The solvers were improved to adapt them for the usage with the particle ensembles characterized by the high rate of the input and output particle flows. Having performed a number of testing simulation runs, it has been shown that the proposed model can be applied for both research and benchmarking purposes.