Despite advances in Computer-Aided Design (CAD) and the evolution of the graphical user interfaces, rapid creation, editing and visualization of three-dimensional (3D) shapes remains a tedious task. Though the availability of Virtual Reality (VR)-based systems allows enhanced three-dimensional interaction and visualization, the use of VR for ab initio shape design, as opposed to ‘importing’ models from existing CAD systems, is a relatively new area of research. Of interest are computer-human interaction issues and the design and geometric tools for shape modeling in a Virtual Environment (VE). The focus of this paper is on the latter i.e. in defining the geometric tools required for a VR-CAD system and in describing a framework that meets those requirements. This framework, the Virtual Design Software Framework (VDSF) consists of the interaction and design tools, and an underlying geometric engine that provides the representation and algorithms required by these tools. The geometric engine called the Virtual Modeler uses a graph-based representation (Shape-Graph) for modeling the shapes created by the user. The Shape-Graph facilitates interactive editing by localizing the effect of editing operations and in addition provides constraint-based design and editing mechanisms that are useful in a 3D interactive virtual environment. The paper concludes with a description of the prototype system, called the Virtual Design Studio (VDS), that is currently being implemented.1.