The development of algorithms for the spatial transformation and registration of tomographic brain images is a key issue in several clinical and basic science medical applications, including computer-aided neurosurgery, functional image analysis, and morphometrics. This paper describes a technique for the spatial transformation of brain images, which is based on elastically deformable models. A deformable surface algorithm is used to find a parametric representation of the outer cortical surface and then to define a map between corresponding cortical regions in two brain images. Based on the resulting map, a three-dimensional elastic warping transformation is then determined, which brings two images into register. This transformation models images as inhomogeneous elastic objects which are deformed into registration with each other by external force fields. The elastic properties of the images can vary from one region to the other, allowing more variable brain regions, such as the ventricles, to deform more freely than less variable ones. Finally, the framework of prestrained elasticity is used to model structural irregularities, and in particular the ventricular expansion occurring with aging or diseases, and the growth of tumors. Performance measurements are obtained using magnetic resonance images.