To maintain the structural integrity of fuel elements for a high temperature gas-cooled reactor (HTGR) under beyond design conditions, strong and oxidation-resistant fuel elements should be further developed. The HTGR fuel elements employ a hot-pressed silicon carbide (SiC)/carbon (C) mixed matrix to improve the oxidative resistance. Hot-press conditions such as pressure, temperature, and duration would be one of the factors that affect the strength of the HTGR fuel elements. To identify the optimal hot-press conditions for preparing the high-strength fuel elements, modeling their effects on the mechanical-strength properties of the HTGR fuel elements should be evaluated quantitatively. In this study, the response–surface model, which represents the relationship between the hot-press conditions and the mechanical-strength properties, has been constructed by introducing statistical design of experiments approaches. The model estimated the optimal hot-press conditions for producing the high-strength fuel elements. We discuss the model’s validity by comparing its predictions with experimental observations.