In multi-hop wireless networks, we often encounter a situation where there are some candidate paths between source node S and destination node D, and have to choose a path from the candidates. Although ordinary routing protocols select paths with minimum hops, QoS (Quality of Service) routing protocols evaluate paths using measures of QoS, such as expected transmission count (ETX). In multi-hop wireless networks with QoS routing, it is an important issue to identify and characterize the best path from the viewpoint of network design. To do this, in [1], we proposed an approximate method to theoretically compute minimum route ETX in static one-dimensional random multihop wireless networks, and in [2], we theoretically identified the best path and gave an exact formula to compute minimum route ETX in static lattice multi-hop wireless networks. In this paper, we propose a new approximate method to theoretically analyze minimum route ETX in a two-dimensional random network. In this method, we extend the approximate method proposed in [1] to be used for two-dimensional random networks. We show this approximate method well describes minimum route ETX by comparing the numerical results of the theoretical methods and simulation results. ©2009 IEEE.