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In this study, pentamode metamaterials were proposed for thermal stress accommodation of alkali metal heat pipes. Sodium/Inconel 718 heat pipes with and without pentamode metamaterial reinforcement were designed and fabricated. Then, these heat pipes were characterized by startup tests and thermal response simulations. It was found that pentamode metamaterial reinforcement did not affect the startup properties of sodium/Inconel 718 heat pipes. At 650–950 °C heating, there was a successful startup of heat pipes with and without pentamode metamaterial reinforcement, displaying uniform temperature distributions. A further simulation indicated that pentamode metamaterials could accommodate thermal stresses in sodium/Inconel 718 heat pipes. With pentamode metamaterial reinforcement, stresses in the heat pipes decreased from 12.9–62.1 to 10.2–52.4 MPa. As a result, sodium/Inconel 718 heat pipes could be used more confidently. This work was instructive for the engineering application of alkali metal heat pipes.