Extended generalized shuffle (EGS) networks are a wide class of interconnection networks introduced by Richards (1993). In this work, we study the blocking performance of EGS networks under point-to-multipoint traffic. Two new routing algorithms for multicast connections in EGS networks are defined, and a theorem proving that these algorithms construct minimum-cost connection trees is enclosed. Simulation results show that the blocking performance of EGS networks under multicast traffic is much better than that of three-stage Clos networks of equal complexity.