ATM networks are expected to efficiently provide multicast communication services such as video conferencing by means of feasible multicast routing algorithms. Several minimum-cost multicast routing algorithms with various degrees of computational complexity have been proposed. These algorithms, however, could be inappropriate for ATM networks due to their high complexities. In this paper, we initially present an optimal multicast routing algorithm, called LOPT (Load Optimal), which guarantees minimum load or a minimum number of cells to be generated throughout the network. LOPT simply corresponds to a minimum-cost multicast routing algorithm if the cost of each link is assumed to be unity. The algorithm efficiently determines the minimum-load multicast route by means of partition. Complexity analysis shows its superiority over the Balakrishnan's algorithm, one of promising multicast routing algorithms, especially when the number of destinations is much smaller than the size of the network. Experimental results further exhibit even better efficiency than its theoretical results. Moreover, based on LOPT, we further propose two variants of the algorithm for applications with different requirements. The first variant determines the multicast route satisfying the condition min[max(delay)] subject to the constraint of the minimum load. The second variant determines the minimum-load route subject to the constraint of a delay bound. The former can be applied for load-sensitive networks, whereas the latter can be applied for delay-sensitive applications.