A performance prediction method is presented, which accurately predicts the expected program execution time on massively parallel systems. We consider distributed-memory architectures with SMD nodes and a fast communication network. The method is based on a relaxed task graph model, a queuing model, and a memory hierarchy model. The relaxed task graph is a compact representation of communicating processes of an appfication mapped onto the target machine. Simultaneous accesses to the resources of a multi-processor node are modeled by a queuing network. The execution time of the appfication is computed by an evaluation algorithm. An example application implemented on a massively parallel computer demonstrates the high accuracy of our model. Furthermore, two applications of our accurate prediction method are presented.