Relay has been incorporated into standards of wireless access networks to improve the system capacity and coverage. However, the resource allocation problem to support scalable video coding (SVC) multicast for wireless relay networks is challenging due to the existence of relay stations (RSs). In this paper, we study the resource allocation problem for SVC multicast over multi-hop wireless relay networks to maximize the total utility of all users with a general non-negative, non-decreasing utility function. Since the problem is NP-hard, we simplify it with RS specification functions which specialize the relay station to receive data for each user, and convert the resource allocation problem with one RS specification function as finding a maximum spanning sub-tree of a directed graph under budget constraint. A heuristic algorithm is proposed to solve the problem with polynomial time complexity. The simulation results reveal that the proposed algorithm outperforms other algorithms under assumptions of two-hop wireless relay networks or separated transmission for relay and access links, and it keeps good approximation to the optimal results.