Group communication is a kind of multicast where each member of a group is allowed to both send and receive multicast messages in the group. Group channel is a communication channel used for group communication. At group channel establishment, routing is required to select routes connecting all group members. The group channel routing needs to generate a set of routing trees, one for each group member, to multicast messages to the group. The traditional method is to generate each of this set of trees independently from the others and each of the trees is made optimal in terms of network cost. However, the overall cost of the set of optimal trees may not be optimal. This paper proposes an algorithm for generating a set of routing trees, which aims at making the overall cost of the set of routing trees of a group channel minimum. Simulations have been done to compare our algorithm with the traditional method in various network situations. © 1998 Published by Elsevier Science Inc. All rights reserved.