We study the resource allocation problem and call admission problem for multicast applications in ATM networks. Two approaches are proposed for dividing the end-to-end QoS requirement into the local QoS constraint on each link of the multicast tree. The first approach is to apply the greedy method to divide the end-to-end QoS based on the residual capacity on the links. In the second approach we show how to use a genetic algorithm to solve the QoS allocation problem. The effective bandwidth concept is used for estimating the amount of bandwidth required to guarantee a certain level of QoS on each link. If the end-to-end QoS cannot be guaranteed due to insufficient network resources, the multicast request is rejected (as a result of call admission). A new performance metric, fractional reward loss, is adopted for evaluating the solutions generated by the proposed two approaches. Our experiment results show that our approaches yield lower fractional reward loss and utilize the network resources more efficiently.