Swelling of clay–sulfate rocks is a serious and devastating geo-hazard, often causing damage to geotechnical structures. Therefore, understanding underlying swelling processes is crucial for the safe design, construction, and maintenance of infrastructure. Planning appropriate countermeasures to the swelling problem requires a thorough understanding of the processes involved. We developed a coupled hydro-mechanical (HM) model to reproduce the observed heave in the historic city of Staufen in south-west Germany, which was caused by water inflow into the clay–sulfate bearing Triassic Grabfeld Formation (formerly Gipskeuper = “Gypsum Keuper”) after geothermal drilling. Richards’ equation coupled to a deformation process with linear kinematics was used to describe the hydro-mechanical behavior of clay–sulfate rocks. The mathematical model is implemented into the scientific open-source framework OpenGeoSys. We compared the model calculations with the measured long-term heave records at the study site. We then designed a sensitivity analysis to achieve a deeper insight into the swelling phenomena. The synthetic database obtained from the sensitivity analysis was used to develop a machine learning (ML) model, namely least-squares boosting ensemble (LSBoost) model coupled with a Bayesian optimization algorithm to rank the importance of parameters controlling the swelling. The HM model reproduced the heave observed at Staufen with sufficient accuracy, from a practical point of view. The ML model showed that the maximum swelling pressure is the most important parameter controlling the swelling. The other influential parameters rank as Young’s modulus, Poisson’s ratio, overburden thickness, and the initial volumetric water content of the swelling layer.