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We present a novel framework based on hidden Markov models (HMMs) for matching feature point sets, which capture the shapes of object contours of interest. Point matching algorithms provide effective tools for shape analysis, an important problem in computer vision and image processing applications. Typically, it is computationally expensive to find the optimal correspondence between feature points in different sets, hence existing algorithms often resort to various heuristics that find suboptimal solutions. Unlike most of the previous algorithms, the proposed HMM-based framework allows us to find the optimal correspondence using an efficient dynamic programming algorithm, where the computational complexity of the resulting shape matching algorithm grows only linearly with the size of the respective point sets. We demonstrate the promising potential of the proposed algorithm based on several benchmark data sets.