This paper proposes a method for detecting instances of shape classes that exhibit variable structure. The term "variable structure" is used to characterize shape classes in which some shape parts can be repeated an arbitrary number of times, some parts can be optional, and some parts can have several alternative appearances. Existing computer vision methods cannot be applied for detecting such shape classes in cluttered images; current methods, including deformable model methods, are only applicable to shapes of fixed (even if non-rigid) structure, i.e., shapes that can be decomposed into a fixed, a priori known, number of shape parts. In this paper, Hidden State Shape Models are introduced, a class of models for shapes with variable structure. A detection method is presented for finding instances of such shapes in images with large amounts of clutter. Our method finds the globally optimal set of correspondences between the model and image features. The detection algorithm o...