Swelling pressure is crucial in the structural design of high-level nuclear waste repositories and foundations. These repositories are typically located at depths between 1000 and 1500 m and are exposed to substantial geodetic stress due to their underground positioning. The entrance of groundwater, which often contains large quantities of ionic salts, causes swelling pressure, complicating the geodetic stresses already exist. To ensure the long-term mechanical stability of these repositories, it is essential to accurately evaluate the swelling pressure of bentonites under such chemically demanding conditions. In this study, nonlinear machine learning algorithms were employed to predict the swelling pressure of bentonites. Input parameters were identified through a correlation matrix, which revealed that swelling pressure is positively correlated with dry density and negatively correlated with salt concentration. The performance of the machine learning models was evaluated using four statistical metrics, i.e., mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and the coefficient of determination (R2). The ANN-stacked tree model outperformed other tested models in predicting swelling pressure, demonstrating an MAE of 0.90 MPa and an R2 of 0.91. These results suggest that machine learning techniques can be highly effective in predicting the behavior of bentonites under complex environmental conditions, contributing to the safe design of nuclear waste storage facilities.