Image metamorphosis, or image morphing, is a popular technique for creating a smooth transition between two images. For synthetic images, transforming and rendering the underlying three-dimensional (3D) models has a number of advantages over morphing between two pre-rendered images. In this paper we consider 3D metamorphosis applied to volume-based representations of objects. We discuss the issues which arise in volume morphing and present a method for creating morphs. Our morphing method has two components: first a warping of the two input volumes, then a blending of the resulting warped volumes. The warping component, an extension of Beier and Neely's image warping technique to 3D, is feature-based and allows fine user control, thus ensuring realistic looking intermediate objects. In addition, our warping method is amenable to an efficient approximation which gives a 50 times speedup and is computable to arbitrary accuracy. Also, our technique corrects the ghosting problem present in Beier and Neely's technique. The second component of the morphing process, blending, is also under user control; this guarantees smooth transitions in the renderings.