The experimental quantification of the swelling pressure is a critical aspect in the design of civil infrastructures passing through potentially swelling formations. This area of study also extends to other applications (e.g., geothermal energy and CO2 sequestration), where underestimating swelling pressure can lead to well instability, as well as in nuclear waste disposal, where accurate estimation of the swelling potential is crucial for characterizing the host rocks. In geomaterials such as clayey rocks, swelling pressures can reach values in the order of several MPa, up to tens of MPa. At such stress levels, the stiffness of the testing device can significantly influence the measurement. This paper presents the development of a model that accounts for the effect of the testing device's stiffness on the swelling pressure measurement. The model has been validated through an experimental study on clayey rock samples, which involved performing oedometer tests and measuring swelling pressures in both axial and radial directions with a device of known stiffness characteristics.