The topological design of distributed packet switched networks consists of finding a topology that minimizes the communication costs by taking into account a certain number of constraints such as the delay and the reliability. This paper proposes a genetic algorithm (GA) for generating low-cost feasible computer network topologies subject to these constraints. The implementation of this algorithm has been subjected to extensive tests in order to measure the quality of solutions. Computational results confirm the efficiency of the GA to provide good solutions for medium-sized computer networks, in comparison with well-tried conventional methods.