Swelling pressure is one of the key parameters in the design of high-level nuclear waste repositories. These repositories are located at a depth of 1000–1500 m from the ground, which causes high geodetic stress. The geodetic stresses are confronted by the development of swelling pressure that takes place due to the ingress of groundwater which consists of high ionic salt concentrations. Therefore, it becomes mandatory to evaluate the swelling pressure of bentonites under these high chemical loadings to ensure the mechanical stability of the repository. In this study, the swelling pressure of bentonites has been evaluated using machine learning (linear and nonlinear) algorithms. The input parameters selected for the estimation of swelling pressure are obtained based on the correlation matrix. The correlation matrix shows that the swelling pressure is highly correlated with dry density (positive correlation) and salt concentration (negative correlation). The performance of machine learning models has been evaluated using four statistical parameters i.e., mean absolute error, mean squared error, root mean squared error, and coefficient of determination. The tree-based nonlinear machine learning algorithm was found to be suitable for the estimation of swelling pressure with a mean absolute error of 0.90 MPa and a coefficient of determination equal to 0.91.