We present a new shape prior segmentation method using graph cuts capable of segmenting multiple objects. The shape prior energy is based on a shape distance popular with level set approaches. We also present a multiphase graph cut framework to simultaneously segment multiple, possibly overlapping objects. The multiphase formulation differs from multiway cuts in that the former can account for object overlaps by allowing a pixel to have multiple labels. We then extend the shape prior energy to encompass multiple shape priors. Unlike variational methods, a major advantage of our approach is that the segmentation energy is minimized directly without having to compute its gradient, which can be a cumbersome task and often relies on approximations. Experiments demonstrate that our algorithm can cope with image noise and clutter, as well as partial occlusions and affine transformations of the shape.