Breast compression simulation is essential for accurate image registration from 3D modalities to X-ray procedures like mammography. It accounts for tissue shape and position changes due to compression, ensuring precise alignment and improved analysis. Although Finite Element Analysis (FEA) is reliable for approximating soft tissue deformation, it struggles with balancing accuracy and computational efficiency. Recent studies have used data-driven models trained on FEA results to speed up tissue deformation predictions. We propose to explore Physics-based Graph Neural Networks (PhysGNN) for breast compression simulation. PhysGNN has been used for data-driven modelling in other domains, and this work presents the first investigation of their potential in predicting breast deformation during mammographic compression. Unlike conventional data-driven models, PhysGNN, which incorporates mesh structural information and enables inductive learning on unstructured grids, is well-suited for capturing complex breast tissue geometries. Trained on deformations from incremental FEA simulations, PhysGNN’s performance is evaluated by comparing predicted nodal displacements with those from finite element (FE) simulations. This deep learning (DL) framework shows promise for accurate, rapid breast deformation approximations, offering enhanced computational efficiency for real-world scenarios.