Lamb’s method in the theory of the plate is extended to the case in which one of the surfaces is not free. The resulting determinantal relation is similar to that of Sezawa. It is then simplified and special cases of the frequency‐velocity relation are discussed. Even when the thickness of the layer is as small as a wave length, the interaction of the upper and lower boundaries of the layer is quite slight and Rayleigh waves and Stoneley’s waves may be discussed separately. A few points in connection with the application of this frequency relation to the ground roll problem are also discussed.