Effective application of wireless sensor networks requires several years of longevity of the battery-powered sensor nodes. Many energyefficient routing protocols have been developed on this account, most of which consider sensor networks with arbitrary mesh topologies. For some applications, however, the assumption of a roughly linear deployment of the sensor modules is more appropriate as it becomes apparent in structure health monitoring of pipelines or bridges. This article introduces Minimum Energy Relay Routing (MERR), a novel approach to energy-efficient routing in sensor networks with linear topology. Conventional routing strategies are discussed, and the structure of routing paths with minimum energy consumption is illustrated. The results of stochastic analyses as well as simulations show that MERR reduces energy consumption significantly compared to existing approaches and performs close to the theoretical optimum for viable sensor distributions.