The interference principle of wave guide propagation is applied to the derivation of the period equations for a number of problems involving both elastic and liquid strata. In the case of undamped steady state propagation in a solid or liquid stratum two arbitrarily chosen points at the same depth must be indistinguishable on an amplitude basis. This well known principle combined with the knowledge of the reflection coefficients enables us to derive in a few simple steps the period equations for a number of multilayer cases which heretofore had been avoided on account of algebraic difficulties. The period equations obtained by this method exhibit a singular simplicity and unity of form. As a consequence of this one may distinguish formally the M 1 and M 2 waves discovered by Sezawa and understand their physical significance.