Network virtualization technology plays a key role in cloud computing, which serves as an effective approach for provisioning a flexible and highly adaptable shared substrate network to satisfy the demands of various applications or services. Recently, the problem of mapping a virtual network (VN) onto a substrate network has been addressed by various algorithms. However, these algorithms are typically efficient for unicast service-oriented virtual networks, and generally not applicable to multicast service-oriented virtual networks (MVNs). Furthermore, the survivable MVN mapping (SMVNM) problem that considers the survivability of MVN has not been studied and is also the focus of this work. In this research, we discuss SMVNM problem under regional failures in the substrate network and propose an efficient algorithm for solving this problem. We first propose a framework and formulate the SMVNM problem with the objective of minimizing mapping cost by using mixed integer linear programming. Then we design an efficient heuristic to solve this problem and introduce several optimizations to achieve the better mapping solutions. We validate and evaluate our framework and algorithms by conducting extensive simulations on different realistic networks under various scenarios, and by comparing with existing approaches. Our simulation experiments and results show that our approach outperforms existing solutions.