We present a hardware-accelerated method for rendering high quality, antialiased shadows using the shadow map approach. Instead of relying on dedicated hardware support for shadow map filtering, we propose a general rendering algorithm that can be used on most graphics workstations. The filtering method softens shadow boundaries by using a technique called percentage closer filtering which is commonly used in software renderers, e.g ray tracing. In this paper we describe how the software algorithm can be efficiently mapped to hardware. In order to achieve realtime or at least interactive frame rates we also propose a slightly modified shadow filtering method that saves valuable hardware resources while still achieving good image quality.