A hybrid model was developed for the analysis of constrained‐layer damping whereby the base plate is described by exact elasticity theory, while the elastomer and constraining layers are analogous to Kerwin's model [J. Acoust. Soc. Am.31, 952–962 (1959)]. Under fluid loading, the success of the technique is measured by a damping efficiency, the ratio of loss in the elastomer to the total loss due to viscoelastic and radiation damping. This efficiency is usually evaluated by combining the viscoelastic loss from a composite plate in vacuum, for antisymmetric and symmetric waves separately with the radiation loss from a single fluid‐loaded plate. This assumes simple addition of the two effects for a fluid‐loaded constrained plate. Extension of the hybrid model to include fluid loading shows that at higher frequencies the presence of the two types of waves redistributes the energy across the plate, invalidating the presumed additive property. Thus it proves necessary to compute damping efficiency from analysis of the fluid‐loaded composite plate with inclusion of both antisymmetric and symmetric waves. [Work supported by the ONR.]