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Geographic routing has been considered as an efficient, simple, and scalable routing protocol for wireless sensor networks since it exploits pure location information to route data packets toward a static sink. Recently, a number of research works have shown that mobile sinks can achieve high energy efficiency and load balance than static ones. To support sink mobility, the location of a mobile sink must be disseminated to the source in a real time manner. However, frequent location update of mobile sinks may lead to both rapid energy consumption of sensor nodes and increased collisions in wireless transmissions. In this paper, we propose a novel location update scheme termed as Elastic Routing for mobile sinks to address this issue. The proposed scheme takes advantage of wireless broadcast transmission nature of wireless sensor nodes. When a sink moves, the new location information is propagated to the source along the reverse geographic routing path during data delivery. Analysis and simulation results indicate that Elastic Routing is superior to the existing solutions in terms of control overhead, data delivery de-lay, and energy consumption.