Prestressed concrete continuous rigid-frame bridges are widely used in infrastructure construction due to their excellent engineering performance. In the traditional design process, engineers need to perform complex numerical calculations to determine the mechanical properties of the structure, which requires a high level of expertise. This study innovatively employs the CatBoost model to construct a predictive model for the mechanical performance of pre-stressed concrete continuous rigid-frame bridges. A training dataset is generated through finite element simulation, and a Bayesian optimization algorithm is introduced to automatically tune the hyperparameters of the model. The research focuses on establishing prediction models for the maximum stress, vertical displacement, and lateral displacement at key locations such as the main piers and mid-span. The results demonstrate that the CatBoost model exhibits excellent predictive performance on the test set. Compared to traditional machine learning models such as Support Vector Regression (SVR) and Decision Tree (DT), the CatBoost algorithm shows significant improvements in both prediction accuracy and robustness. Through interpretability techniques such as SHAP analysis and Partial Dependence Plots (PDP), this study further reveals the influence of key parameters-including Unit Weight of Concrete, initial tensile control stress, concrete elastic modulus, pre-stress loss, and uneven foundation settlement on mechanical performance.