The heat pipe reactor represents a promising high-temperature microreactor design comprising heat pipes, fuel rods, and monoliths. Prolonged operation at elevated temperatures leads to an obvious thermal creep and thermal stress within the monolith. The monolith may have structural failure due to creep damage and fatigue damage caused by temperature fatigue load. This paper presents an analysis of the creep fatigue damage in the monolith of the MegaPower heat pipe reactor using the American Society of Mechanical Engineers (ASME), Boiler and Pressure Vessel Code Section III, Division 5 (BPVC Sec. III, Div. 5) inelastic design-by-analysis rules. The research findings demonstrate pronounced stress relaxation in the monolith caused by thermal creep, resulting in a redistribution of thermal stress. The region experiencing peak thermal stress within the monolith transitions from the thinnest web between the fuel rods to the edge of the monolith after 50 000 h of operation at full power. Thermal creep results in a 40.5% decrease in peak thermal stress and a 0.023% increase in the displacement amplitude of the monolith. The creep fatigue damage in the monolith at full power for 50 cycles, each lasting 1000 h, adheres to the design rule limitation of the ASME BPVC. The damage is primarily concentrated in the thinnest web region at the edge of the monolith, predominantly attributed to creep damage. The creep fatigue damage check in the monolith should carefully consider the effect of stress relaxation.