A numerical model is used to derive both the S2 and M3 tides for the shelf seas around the British Isles. The M2 tide was run with the S2 tide in the presence of quadratic friction. It was found that quadratic friction marginally overdamps the S2 tide. A further approximate representation of the S2 tide was obtained from a model in which the quadratic friction term was replaced by a linear frictional coefficient in a tensor form based upon the M2 tidal currents derived from the spring-neap simulation. These simulations form the basis for interpreting the M2/S2 ratios and phase differences that occur on the north-west European shelf.