In recent years the increased use of 3D scanning hardware has introduced a new type of data to the design and manufacturing field. In many design and manufacturing applications (e.g., part refurbishing or remanufacturing) a scanned 3D model may be provided as an input to a shape matching system to search the database for related or identical models with the purpose of extracting useful information. The introduction of scanned 3D models restricts the use of the CAD-based 3D model search and comparison methods due to significant differences in model representations. The CAD models provide structured and high-level representation of the part features, whereas the scanned 3D models usually come in a polygonal mesh representation, which does not directly reveal engineering features of the part. These differences require new algorithms for comparing the shapes of scanned 3D models, ones that are robust against different scanning technologies and can be adjusted to work with different representations of the models. In this paper, a new approach and algorithms for scanned 3D shape matching and comparison are presented. Given the scanned 3D model as an input the approach first uses general-purpose shape matching methods to identify a small list of likely matches (i.e., candidate models) for more detailed shape comparison. To perform detailed comparison of the shapes each candidate model is geometrically adjusted (i.e., rotated and translated) with the input using one of two new viewpoint algorithms developed in this paper. Once the candidate models are adjusted they are compared to the input to identify the similarities and differences between their shapes. To accomplish this task a new 3D shape matching algorithm is developed. The relevance of the methodology developed in this paper is illustrated with the application of scanned 3D shape matching and comparison algorithms in rapid manufacturing of broken parts.