Carrier-grade networks have often multiple layers of protocols. To tackle this heterogeneity, the Pseudo-Wire architecture provides encapsulation and decapsulation functions of protocols over Packet-Switched Networks. At the scale of multi-domain networks, computing a path to support an end-to-end service requires various encapsulations and decapsulations that can be nested but for which manual configurations are needed. Graph models are not expressive enough for this problem. In this paper, we propose an approach using graphs and Push-Down Automata (PDA) to capture the compatibility among encapsulations and decapsulations along an inter-domain path. They are respectively modeled as pushes and pops on a PDA’s stacks. We provide polynomial algorithms that compute either the shortest path in hops, or in the number of encapsulations and decapsulations to optimize interfaces’ configuration.