Volume rendering is a computational challenge even for todays high performance computers. In the field of supercomputing there is a trend towards massively parallel machines with distributed memory architectures. The algorithm presented here is capable of exploiting the processing power of such machines most efficiently. Arbitrary viewing directions are supported without the need for dynamic data redistribution during rendering. Nevertheless, only small amounts of volume data have to be replicated in local processor memories. A scheme is presented for accumulating partial images generated locally on each processor which avoids the bottleneck problems of previous approaches. We report on an implementation of this renderer on a distributed memory machine with 1024 processors connected in a hypercube topology.