In image-guided surgery it is necessary to align preoperative image data with the patient. The rigid-body approximation is usually applied, but is often not valid due to tissue deformation. Non-rigid deformation algorithms have been applied to related, but not identical problems, such as atlas matching and surgery simulation. In image-guided surgery we have the additional information that the deformation is constrained by the physical properties of the different tissues. The most important properties that must be incorporated are the rigidity of bone, the unconstrained nature of fluid regions and the relatively smooth deformation of soft tissue. Hence, we have developed a simplified model of tissue deformation based on a three-component system. Rigid regions are constrained by the rigid-body transformation and fluid regions are unconstrained. A number of energy models for deformable tissues have been compared. The model can be deformed using intraoperative data, in this case landmarks, using a technique similar to active contours. A novel strategy to avoid folding in the transformation is described. Our method was applied to MRI and CT data from a neurosurgery patient with epilepsy. Although the current implementation is only two dimensional, the initial results are promising. As the algorithm must ultimately run in or near 'real-time' an improved implementation of the energy minimization is underway. This paper presents the problem of tissue deformation, which has received little attention in the literature and outlines the framework we have developed for tackling this difficult subject.