Sound transmission through a fluid layer which is imbedded in lighter density fluid is analyzed in terms of a resonant transmission theory. Expressions for the transmission coefficient (T) have been obtained indicating that T can be decomposed into resonance terms corresponding to symmetric and antisymmetric propagation modes in the layer. A computer progarm is utilized to compute both total T and T for each resonance for several cases of interest. Dispersion curves for the layer are obtained and compared to calculations and experimental data in the literature. The resonance widths are also calculated and an interpretation of total T as a function of angle of incidence and frequency thickness product is made in terms of these individual resonances. A similar but more complicated analysis holds for the elastic plate.