The computation of soft shadows created by area light sources is a well-known problem in computer graphics. Due to the complexity of the problem, soft shadows commonly are generated only for images that are rendered in an off-line process. In interactive virtual environments, where images have to be computed in real time, soft shadows are mostly replaced by hard shadows as this takes much less time to compute. This paper presents an algorithm that uses a geometrical method to generate a triangulated approximation of the soft shadow cast by a polygonal object very quickly. The algorithm can simulate effects such as the varying width of penumbras depending on distance to the light and can be extended to support non-convex light sources as well. We mention the artifacts arising from triangulation and give discuss how to alleviate such problems.