G. I. Taylor's approximate analytical solution for the tidal flow in the Severn estuary is extended to find the optimum location for a tidal power barrage, from the power point of view. It appears to be at the lowest point in the estuary, between Ilfracombe and Gower – contrary to earlier computations. The analytical solution shows that barrages radiate tidal waves out to sea, which highlights the important role of the far-field boundary condition in absorbing them. This appears to have been neglected in numerical models, which may explain the difference from the earlier results.