Space fission power systems can enable ambitious solar-system and deep-space science missions. The heat pipe cooled reactor is one of the most potential candidates for near-term space power supply, featured with safety, simplicity, reliability, and modularity. Heat pipe cooled reactors are solid-state and high temperature (up to 1500 K) reactors, where the thermal expansion is remarkable and the mechanical response significantly influences the neutronics and thermal analyses. Due to the considerable difference between heat pipe cooled reactors and traditional water reactors in the structure and design concept, the coupling solutions for light water reactors cannot be directly applied to heat pipe cooled reactor analyses. Therefore, new coupling framework and program need to consider the coupling effects among neutronics, heat transfer as well as mechanics. Based on the Monte Carlo program RMC and commercial finite element program ANSYS Mechanical APDL, this work introduces the three coupling fields of neutronics (N), thermal (T), and mechanics (M) for heat pipe cooled reactors. The neutronic and thermal-mechanical (N/T-M) coupling strategy is developed theoretically, focusing on the formulation of the nonlinear problem, iteration schemes, and relaxation methods. Besides, the finite element method and the Monte Carlo program use different meshes and geometry construction methods. The spatial mapping and geometry reconstruction are also essential for the N/T-M coupling, which is discussed and established in detail. Furthermore, the N/T-M coupling methods are applied to the preliminary self-designed 10 kWe space heat pipe cooled reactor. Coupling shows that the thermal-mechanical feedback in the solid-state reactor has negative reactivity feedback (−2007 pcm) while it has a deterioration in heat transfer due to the expansion in the gas gap.