In recent years, 3D media have become more and more widespread and have been made available in numerous online repositories. A systematic and formal approach for representing and organizing shape-related information is needed to share 3D media, to communicate the knowledge associated to shape modeling processes and to facilitate its reuse in useful cross-domain usage scenarios. In this paper we present an initial attempt to formalize an ontology for digital shapes, called the Common Shape Ontology (CSO). We discuss about the rationale, the requirements and the scope of this ontology, we present in detail its structure and describe the most relevant choices related to its development. Finally, we show how the CSO conceptualization is used in domain-specific application scenarios.