We have developed a biomechanical model of the breast to simulate compression during mammographic imaging. The modelling framework was applied to a set of MR images of the breasts of a volunteer. Images of the uncompressed breast were segmented into skin and pectoral muscle, from which a finite element (FE) mesh of the left breast was generated using a nonlinear geometric fitting process. The compression plates within the breast MR coil were used to compress the volunteer's breasts by 32% in the latero-medial direction and the compressed breasts were subsequently imaged using MRI. The FE geometry of the uncompressed left breast was used to numerically simulate compression based on finite deformation elasticity coupled with contact mechanics, and individual-specific tissue properties. Accuracy of the simulated FE model was analysed by comparing the predicted surface data, and locations of three internal features within the compressed breast, with the equivalent experimental observations. Model predictions of the surface deformation yielded a RMS error of 1.5 mm. The Euclidean errors in predicting the locations of three internal features were 4.1 mm, 4.1 mm and 6.5 mm. Whilst the model reliably reproduced the compressive deformation, further investigations are required in order to test the validity of the underlying modelling assumptions. A reliable biomechanical model will provide a multi-modality imaging registration tool to help identify potential tumours observed between mammograms and other imaging modalities such as MRI or ultrasound.