Multicast is an important interprocessor communication pattern existing in various parallel application algorithms. This paper proposes a new multicast algorithm for hypercube computers that not only minimizes the number of hops required for delivery of the message and keeps the amount of traffic small, but also takes into consideration of balancing traffic among the active processors to maximize the parallelism in communication. Our algorithm has a time complexity of O(nN) for fault-tolerant multicasting in a hypercube of N = 2 n processors containing an arbitrary number of faulty processors.