This paper is devoted to the problem of mapping parallel computations to distributed systems based on RapidIO communications. A distributed system is represented as a set of hosts with given levels of performance and a set of switches interconnected by links with known bandwidths. Parallel computation is specified as a number of processes that communicate by passing data streams. Each process requires certain performance and each data stream requires certain network bandwidth. It is necessary to map processes to hosts, as well as define routes for data streams and routing tables for switches, in such a way that the performance requirements of processes and bandwidth requirements of data streams are met. In general, this task is NP-complete. We propose an approach based on integer linear programming (ILP) methods that provides correct mapping of parallel computations to a distributed system and enables optimization of the map with respect to a number of parameters.