In the last few years, the volume of multimedia content available on the Web significantly increased. This led to the need for techniques to handle such data. In this context, we see a growing interest in considering the Semantic Web in action and in the definition of tools capable of analyzing and organizing digital shape models. In this paper, we present a Semantic Web environment, be-SMART, for inspecting 3D shapes and for structuring and annotating such shapes according to ontology-driven metadata. Specifically, we describe in details the first module of be-SMART, the Geometry and Topology Analyzer, and the algorithms we have developed for extracting geometrical and topological information from 3D shapes. We also describe the second module, the Topological Decomposer, which produces a graph-based representation of the decomposition of the shape into manifold components. This is successively modified by the third and the fourth modules, which perform the automatic and manual segmentation of the manifold parts.