Recently it has been suggested that finite element methods could be used to predict breast deformations in a number of applications, including comparison of multimodality images, validation of image registration and image guided interventions. Unfortunately knowledge of the mechanical properties of breast tissues is limited. This study evaluated the accuracy with which biomechanical breast models based on finite element methods can predict the displacements of tissue within the breast in the practical clinical situation where the boundaries of the organ might be known reasonably accurately but there is some uncertainty on the mechanical properties of the tissue. For two datasets, we investigate the influence of tissue elasticity values, Poisson's ratios, boundary conditions, finite element solvers and mesh resolutions. Magnetic resonance images were acquired before and after compressing each volunteer's breast by about 20%. Surface displacement boundary conditions were derived from a three-dimensional nonrigid image registration. Six linear and three nonlinear elastic material models with and without skin were tested. These were compared to hyperelastic models. The accuracy of the models was evaluated by assessing the ability of the model to predict the location of 12 corresponding anatomical landmarks. The accuracy was most sensitive to the Poisson's ratio and the boundary condition. Best results were achieved for accurate boundary conditions, appropriate Poisson's ratios and models where fibroglandular tissue was at most four times stiffer than fatty tissue. These configurations reduced the mean (maximum) distance of the landmarks from 6.6 mm (12.4 mm) to 2.1 mm (3.4 mm) averaged over all experiments.