This research evaluates the accuracy of seven applied compressive stress–strain constitutive models—including the Hogenstad, Saenz, Kent-Park, Popovics, Thorenfeldt, Hajimeh, and Eurocode 2 models—and subsequently proposes a combined model, termed Popovics–Guo, to more precisely predict the stress–strain curve of high-strength rubberized concrete containing high rubber content with varying volumetric replacements of sand by rubber (0%, 20%, 40%, and 60%). Axial compressive tests were performed on cylindrical and cubic specimens to obtain experimental stress–strain curves and to examine both the linear and nonlinear behavior up to the point of maximum strain in the rubberized concrete.The performance of the constitutive models was evaluated using statistical criteria such as RMSE, R², and MAE, in addition to graphical comparisons. The results indicate that, with an increase in rubber content coupled with the high compressive strength of the concrete, the prediction errors of the existing models in various segments of the stress–strain curve increase significantly, resulting in a poor match with the experimental data. Consequently, the suggested combined Popovics–Guo model was introduced, which demonstrated high accuracy in predicting the stress–strain behavior of rubberized concrete in both the ascending and descending branches (with R² values exceeding 0.98 for all rubber replacement percentages). Furthermore, the optimal values of the empirical parameters in the Popovics, Thorenfeldt and suggested Popovics–Guo models for each rubber content, as determined in the mix design of this study, are presented. The findings of this research provide practical guidance for selecting appropriate constitutive models based on the rubber content in concrete and help identify research gaps for the development of future models.