The electrical circuit of a simulator of pulse high voltage overvoltages with an amplitude of up to 10 kV DC, which is intended for testing the stability of solid-state power converters to emergency conditions according to item 4.9.3.5 of State Standard GOST 33726-2016, is proposed. By using the developed simulator, a high voltage pulse with the required values of amplitude, duration, and rising and falling rates can be obtained. Analytical expressions are derived that describe, with sufficient accuracy, the transients in the electrical circuits of the proposed pulse high voltage overvoltage simulator, which is confirmed by computer simulation carried out in the MATLAB Simulink environment. Based on the obtained theoretical results, a mockup simulator for testing the stability of a high-voltage power converter to overvoltage of a given shape and amplitude has been developed. The results of practical use of the developed simulator on the example of testing the PSN110 U1 auxiliary converter are given. The article may be of interest to specialists who design equipment for carrying out overvoltage tests of solid-state high-voltage converters for both railway transport and industrial applications.