This thesis explores the application of physical models in medical image registration and surgery simulation. The continuum models of elasticity and viscous fluids are described in detail, and this knowledge is used as a basis for most of the methods described here. Real-time deformable models for surgery simulation Real-time deformable models, using finite element models of linear elasticity, have been developed for surgery simulation. The time consumption of the finite element method is reduced dramaticly, by the use of condensation techniques, explicit inversion of the stiffness matrix, and the use of selective matrix vector multiplication. Fluid medical image registration A new and faster algorithm for non-rigid registration using viscous fluid models is presented. This algorithm replaces the core part of the original algorithm with multi-resolution convolution using a new filter, which implements the linear elasticity operator. Using the filter results in a speedup of at least an order of magnitude. Use of convolution hardware is expected to improve the performance even more. Mandibular growth for time registration of mandibles Non-rigid registration using a physically valid model of bone growth is also presented. Using medical knowledge about the growth processes of the mandibular bone, a registration algorithm for time sequence images of the mandible is developed. Since this registration algorithm models the actual development of the mandible, it is possible to simulate the development. Rigid medical image registration Rigid image registration using voxel similarity measures are reviewed, and new measures based on Grey Level Cooccurrence Matrices (GLCM) are introduced. These measures are evaluated extensively using CT, MR, and cryosection images from the Visible Human data set. The results show that mutual information remains the best generally applicable measure. But for specific modality combinations the new GLCM measures show considerable promise.