Cloud computing services are realized through the mapping of the service layer network into the physical infrastructure. Multiple failures in the physical infrastructure could disrupt cloud network connectivity and cause cascading failures impacting cloud service customers. As the physical infrastructure has limited resources, most early research works for survivable virtual network mapping were concentrated on the single link failure scenario. In this paper, we study survivable cloud network mapping with multiple physical link failures and a special case, Shared Risk Link Group (SRLG) failure. We present the necessary and sufficient conditions to guarantee a survivable mapping with multiple physical link failures. Corresponding mixedinteger linear programming (MILP) formulations which avoid the enumeration of failure link combinations are proposed. We also provide the corresponding formulations for the SRLG case. Computation results demonstrate the viability of our approaches.