In a multi-tenant cloud, cloud vendors provide services (e.g., elastic load-balancing, virtual private networks) on service nodes for tenants. Thus, the mapping of tenants’ traffic and service nodes is an important issue in multi-tenant clouds. In practice, unreliability of service nodes and uncertainty/dynamics of tenants’ traffic are two critical challenges that affect the tenants’ QoS. However, previous works often ignore the impact of these two challenges, leading to poor system robustness when encountering system accidents. To bridge the gap, this paper studies the problem of robust service mapping in multi-tenant clouds (RSMP). Due to traffic dynamics, we take a two-step approach: service node assignment and tenant traffic scheduling. For service node assignment, we prove its NP-Hardness and analyze its problem difficulty. Then, we propose an efficient algorithm with bounded approximation factors based on randomized rounding and knapsack. For tenant traffic scheduling, we design an approximation algorithm based on fully polynomial time approximation scheme (FPTAS). The proposed algorithm achieves the approximation factor of 2+ $\epsilon$ , where $\epsilon$ is an arbitrarily small value. Both small-scale experimental results and large-scale simulation results show the superior performance of our proposed algorithms compared with other alternatives.