Design/methodology/approach Using finite element method, this study examined four sinusoidal deformable models with 0.08 mm deep cavities under pressures ranging from 0.5 MPa to 640 MPa. The simulation used four-node bilinear elements with a meshing size of 0.005 and reduced integration with hourglass control (CAX4R elements in ABAQUS). The type of contact used is Static General with surface-to-surface interaction. Findings The results of this study align well with previous research, showing that von Mises stress, stress distribution, contact area and deformation increase with higher loads. The model height variations have an insignificant effect on the von Mises stress and contact area parameters. Model height variations have minimal impact on von Mises stress and contact area (less than 3% difference) but significantly affect deformation, with differences exceeding 100% across models. Research limitations/implications The conducted research contains several limitations. This study uses a simplified two-dimensional model instead of a more accurate three-dimensional model for complex contact behaviors; it assumes perfectly elastic materials rather than more complex material properties; and it models conditions without lubrication, which does not reflect real-world scenarios. In future studies, the variation of material properties, effects of lubrication and further loading conditions should be considered to improve the accuracy and applicability of the obtained results. These include repetitive loads, plastic contact and elastic–plastic contact. Originality/value This research is unique because it analyzes the effect of sinusoidal model height variations that have never been done before. This research deepens the understanding of the Saint-Venant principle which is important in designing contact mechanics models. By understanding how model height variations affect contact mechanics, researchers can choose an appropriate model height for analysis while maintaining the accuracy of simulation results in a faster computation. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2024-0285/