A Bayesian network formulation for relational shape matching is presented. The main advantage of the re- lational shape matching approach is the obviation of the non-rigid spatial mappings used by recent non-rigid matching approaches. The basic variables that need to be estimated in the relational shape matching objective function are the global rotation and scale and the lo- cal displacements and correspondences. The new Bethe free energy approach is used to estimate the pairwise correspondences between links of the template graphs and the data. The resulting framework is useful in both registration and recognition contexts. Results are shown on hand-drawn templates and on 2D transverse T1-weighted MR images.