Heat pipes, as passive and efficient heat transfer components, are widely used in aerospace, nuclear energy, and other fields. In heat pipe cooled reactors, heat pipes transfer the heat from the solid reactor core directly to the hot end of the energy conversion device, offering advantages such as compact structure, good transportability, and high inherent safety. This study focuses on heat pipe-cooled reactors with Stirling systems as energy conversion devices, developing a numerical simulation program that integrates the reactor core, heat pipes, and Stirling engines. The program was validated using experimental data from the KRUSTY system under challenging conditions such as reactivity insertion. Results demonstrate excellent agreement between the program's calculations and experimental data from the KRUSTY prototype reactor. The predicted trends for core temperature and output power align well with the experimental observations; The average prediction error for the hot end temperature of the Stirling system is 3.56%, while the average prediction error for power is 2.23%, verifying the accuracy and reliability of the model. This program can provide support for the design and safety analysis of heat pipe cooled space reactors.