In Malignant Pleural Mesothelioma (MPM), solid stress and tissue deformation significantly impact tumour growth and invasion. This study presents a computational framework that integrates biomechanical tumour dynamics, tissue deformation, and force interactions within a realistic anatomical setting. Using the Finite Element Method, the framework is applied to a lung mesh reconstructed from CT scans, incorporating a synthetic mesothelioma tumour with defined material properties. Numerical results from the simulations closely match the analytical solution, with deviations within 5%, confirming the model’s reliability and accuracy. Simulations of point compression and surface expansion effectively capture the localised tumour deformation and lung volume changes, replicating expected breathing mechanics under different conditions. The findings emphasize the role of mechanical interactions in tumour progression, demonstrating how increased tissue stiffness affects deformation patterns and respiratory dynamics. This study establishes a foundation for integrating computational biomechanics with predictive tumour modelling, offering potential applications in personalised medicine for MPM.