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Shape matching between a predefined shape model and an raw image is a key problem in image recognition, which can arise in character recognition, industrial applications, and medical applications. Medical images pose particular difficulties in that the image is noisy, the background is complex, and the shape is flexible. Dynamic programming can be applied to shape matching where the shape model is expressed by a sequence of line segments and the shape is varied by independently changing the length of the line segments. The generated shapes are applied to the raw image at every location. For each shape and location, the average angular similarity between the model segment and the output of an edge-operator applied along the line segment is computed. The optimal criterion is evaluated as the maximum of the similarity function and so forms a natural criterion to evaluate. However, there are a huge number of computations if we calculate by an exhaustive method. In order to decrease the computation while preserving the optimal solution, Dynamic Programming (DP) is introduced. The DP matching method is successfully applied to medical images of microscopic kidney tissue and ultrasonic image sequence showing heart action.