The prime difficulty in research and development of handwritten character recognition systems is the variety of shape deformations. The key to recognizing such complex objects as handwritten characters is through shape descriptions which are robust against shape deformation, together with quantitative estimation of the amount of deformation. In this paper, on the basis of the structural description by Nishida and Mori (1992), we propose a shape matching algorithm and a method for analysis and description of shape transformation for handwritten characters. The object is described in terms of a qualitative and global structure which is robust against deformation, and the description is matched against built-in models. On the basis of the correspondence of components between the object and the model, geometrical and statistical transformations are estimated, and the decision of recognition or rejection is based on the estimations. Structural descriptions and geometrical/statistical transforms are integrated in a systematic way. Experimental results are shown for off-line handwritten numeral recognition and on-line handwriting recognition.