Oil and gas well casings are highly susceptible to failure under conditions of corrosion and deformation. To overcome the long computational times of traditional finite element analysis (FEA) methods, an intelligent stress prediction model for damaged casings is innovatively proposed based on the Improved Grey Wolf Optimizer (IGWO) and CatBoost. High-fidelity finite element (FE) simulation models of the casing were constructed utilizing the secondary development technology of Abaqus. Consequently, a comprehensive stress sample database was established. This database contained various casing types, operating conditions, deformation patterns, and damage severities. A composite chaotic mapping strategy was incorporated to improve the standard Grey Wolf Optimizer. Through this improvement, the susceptibility to local optima was overcome. Thus, the global adaptive tuning of the CatBoost model"s hyperparameters was enabled. Through SHAP analysis, the feature dependencies behind the predictions are clarified, and the decision logic of the data-driven model is verified. A maximum goodness of fit (R2) of 0.9595 is achieved on the test set. An accuracy significantly superior to traditional algorithms is demonstrated. In scenarios with complex corrosion distributions, a prediction error of only 0.45% is observed. Therefore, the accuracy under simulated real-world conditions is validated. The mapping relationship between casing damage and casing stress under complex operating conditions is established. The bottleneck of low computational efficiency inherent in traditional finite element simulations is overcome. Ultimately, an efficient tool integrating physical interpretability with real-time computational performance is provided for the integrity evaluation of oil and gas well strings.