We present a novel approach for automatic segmentation of the myocardium in short-axis MRI using deformable medial models with an explicit representation of thickness. Segmentation is constrained by a Markov prior on myocardial thickness. Best practices from Active Shape Modeling (global PCA shape prior, statistical appearance model, local search) are adapted to the medial model. Segmentation performance is evaluated by comparing to manual segmentation in a heterogeneous adult MRI dataset. Average boundary displacement error is under 1.4 mm for left and right ventricles, comparing favorably with published work.