Many existing image registration methods have difficulties in accurately describing significant rotation and bending of entities (e.g. organs) between two datasets. A common problem in this case is to ensure that the resulting registration is physically plausible, i.e. that the registration describes the actual bending/rotation occurring rather than just introducing expansion in some areas and shrinkage in others. In this work we developed a general framework for deformable image registration of two 3D datasets that alleviates this problem. To ensure that only physically feasible and plausible solutions to the registration problem are found, a soft tissue deformable model is used to constrain the search space for the desired correspondence map while minimizing a similarity metric between the source and reference datasets. Results from a deformable phantom experiment were used to verify and evaluate the framework.