In image synthesis, cloth objects such as clothes are most often modelled as textures mapped onto rigid surfaces. However, in order to represent such objects more realistically, their physical properties must be examined. This paper describes a method for modelling cloth material hanging in three dimensions when supported by any number of constraint points. The cloth synthesized with this model contains folds and appears more realistic than simple texture mapping. This paper also describes a method for rendering the cloth once its free-hanging shape has been determined.The computation of the surface of a free-hanging cloth is performed in two stages. The first stage approximates the shape of the surface which is interior to the constraint points, and the second stage performs a relaxation process on all points on the surface to arrive at a close approximation to its shape. The rendering of the surfaces is done using a ray-tracer which treats the surface as a mesh of line segments.