Growing interest in Virtual Reality (VR) over the past few years has led to the development of VR techniques for applications such as virtual manufacturing, virtual assembly, virtual training, etc. Most of these applications involve the moving of objects and interaction of them with the environment in virtual space. One foreseeable important application of virtual manufacturing is Numerically Controlled (NC) machining path generation and verification in a VR environment. In this application the efficient computation and accurate representation of swept volumes of the machining cutters is an important issue. This paper describes a fast and accurate method for generating the swept volume of a moving object undergoing an arbitrary translational and rotational motion, with application to NC machining simulation in a VR setting. The Sweep Differential Equation (SDE) method, which we initially developed for representing and computing the swept volumes of rigid moving objects and subsequently extended to objects that may deform during the course of motion, forms the basis for the VR application of NC cutter path generation and verification. An example is provided to demonstrate the effectiveness of the SDE method for simulation of multi-axis NC machining.