A variety of smart services are being provided on multiple virtual networks embedded into a common inter-cloud substrate network. The substrate network operator deploys critical substrate nodes so that multiple service providers can achieve enhanced services due to the secure sharing of their service data. Even if one of the critical substrate nodes incurs damage, resiliency of the enhanced services can be assured due to reallocation of the workload and periodic backup of the service data to the other normal critical substrate nodes. However, the connectivity of the embedded virtual networks must be maintained so that the enhanced services can be continuously provided to all clients on the virtual networks. This paper considers resilient virtual network embedding (VNE) that ensures the connectivity of the embedded virtual networks after critical substrate node failures have occurred. The resilient VNE problem is formulated using an integer linear programming model and a distance-based method is proposed to solve the large-scale resilient VNE problem efficiently. Simulation results demonstrate that the distance-based method can derive a sub-optimum VNE solution with a small computational effort. The method derived a VNE solution with an approximation ratio of less than 1.2 within ten seconds in all the simulation experiments.