Shape analysis is an important process for many computer vision applications, including image classification, recognition, retrieval, registration, segmentation, etc. An ideal shape model should be both invariant to global transformations and robust to local distortions. In this work we developed a new shape modeling framework that achieves both efficiently. A shape instance is described by a curvature-based shape descriptor. A Profile Hidden Markov Model (PHMM) is then built on such descriptors to represent a class of similar shapes. PHMMs are a particular type of Hidden Markov Models (HMMs) with special states and architecture that can tolerate considerable shape contour perturbations, including rigid and non-rigid deformations, occlusions, and missing parts. The sparseness of the PHMM structure provides efficient inference and learning algorithms for shape modeling and analysis. To capture the global characteristics of a class of shapes, the PHMM parameters are further embedded into a subspace that models long term spatial dependencies. The new framework can be applied to a wide range of problems, such as shape matching/registration, classification/recognition, etc. Our experimental results demonstrate the effectiveness and robustness of this new model in these different settings. [1]