Any path routing has been proposed as a new routing paradigm for enhancing the performance of Wireless Mesh Networks (WMNs) by exploiting the inherent broadcasting and spatial diversity properties of a wireless medium. This routing paradigm is based on a MAC protocol which provides an any cast transmission capability and therefore allows each node to send its packets to any candidate neighboring node among the forwarding set. Accordingly, this paper proposes an analytical model for investigating the performance of any path routing in respect of end-to-end delay. In this model, the potential MAC-induced Expected Packet Transmission Time (EPTXT) overhead incurred by the nodes in contending for the shared channel resources in order to transmit a packet to its forwarding set is formulated. Based on the EPTXT of a node, the end-to-end delay of the node in delivering a packet to the destination via its forwarding set is then calculated. The numerical results confirm that the proposed analytical approach provides an accurate estimation of the end-to-end delay performance of a node in transmitting a packet along an any path to the destination.