Since the implementation of the first computer networks, a great attention has been given to their topological design, because of the financial aspects of their dimensioning and operating. The high number of possible topological configurations, the discrete character of the link capacity options available in the marketplace, the non- linearity of the cost functions associated with the network topologies, constitute the main factors which make complex this design problem. As a result, only heuristic methods can lead with a reasonable computing effort, to good feasible solutions, but not necessarily optimal. This paper proposes a heuristic method for generating in an economical manner network topologies which satisfy some reliability and quality of service constraints. The implementation of the method has been submitted to a sequence of tests which confirm its robustness and its efficiency according to the quality of solutions provided.