In this thesis, an approach for solving multicast routing problem in computer network based on Genetic Algorithm was used . Due to different applications with many services obtained, in addition to high degree of speed, B-ISDN (Broadband Integrated Service Digital Network) was suggested to be an application example of computer networks. The new services and applications inj this network lead to introduce a multicast routing and switching problem. The link propagation time delay is used as a metric between every two nodes in a network. The worst case for solving the problem is considered as a link failure in a network design. Both Distributed and Centralized traditional routing methods are used to find the shortest paths in a network. A comparison is taken between the results obtained from the implementation of both the traditional methods the suggested one. Reliability and minimum propagation time delay can be achieved from applying the weio approach on many examples of networks.