Ethernet technology is being deployed in metro and wide area networks. However, despite recent evolutions, Ethernet cannot be considered a carrier class technology due mainly to the lack of facilities for efficient traffic engineering (TE). In this article, we propose a Flow-aware TE approach for carrier class Ethernet networks providing services like those defined by the Metro Ethernet Forum. The flow-aware networking approach we consider is based on the Cross-protect router mechanisms, allowing satisfactory quality for streaming and elastic flows without explicitly identifying traffic classes by the combined use of fair queuing and admission control. Our proposal applies specifically to architectures where a tunnel is established between ingress and egress nodes (like Ethernet over MPLS). In this specific context, the Cross-protect mechanisms are applied on a per tunnel basis. We analyze the proposed approach in terms of flow blocking probabilities for which explicit formula are derived. We also extend the study framework to the case where several paths are established between a pair of ingress/egress nodes, and propose a simple load balancing scheme. We analyze its performance and derive approximate formula for the flow blocking probability in this case. The analysis is validated by extensive simulations.