This paper presents a method of determining the swept volume of Non-Uniform rational B-Spline (NURBS) curves and surfaces. Characteristic (also called singular) points or curves are determined by obtaining local and global maxima points at discrete frames during the motion and with respect to a local moving coordinate system. This coordinate system is calculated in reference to the direction of motion of the rigid body as determined from its composite velocity vector. The aim is to develop a rigorous method for identifying and visualizing a NURBS swept volume. NURBS have become the industry standard for the representation, design, and data exchange of geometric information processed by computers. On the other hand, sweeping operations are valuable tools for the CAD user to shape and create primitives. In this paper, we extend our previous method used in determining the swept volume of implicit and parametric surfaces and those that are as a result of multiple sweeping. The method and numerical algorithm are illustrated through examples.