An analytical solution for the transient heat transfer under groundwater flow for ground heat exchangers (GHEs) is presented. The method is an extension of the transient multipole expansion that describes the transient heat transfer as a pure conduction phenomenon inside and around a GHE including arbitrarily positioned pipes in the grout, coupling an irrotational and incompressible potential field in the ground with constant far-field velocity. The method does not rely on the supposition that groundwater flows through the GHE but instead moves around it. The method is validated against a finite element analysis model comparing the borehole wall temperature for two cases considering different single U-tube pipes position. It is shown that the thermal resistances inside the GHE do not respect the general symmetry condition as opposed to the pure conduction problem.