We propose a sweep-based approach to the freeform deformation of three-dimensional objects. Instead of using a volume enclosing the whole object, we approximate only its deformable parts using sweep surfaces. The vertices on the object boundary are bound to the sweep surfaces and follow their deformation. Several sweep surfaces can be organized into a hierarchy so that they interact with each other in a controlled manner. Thus we can support intuitively plausible shape deformation of objects of arbitrary topology with multiple control handles. A sweep-based approach also provides important advantages such as volume preservation. We demonstrate the effectiveness of our technique in several examples. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computational Geometry and Object Modeling]: Curve, surface, solid, and object representations