We quantitatively study the effect that hydrostatic pressures have on the static and dynamic effective material properties of perforated viscoelastic elastomers. A resonance methodology that we had developed earlier is here extended and generalized to account for the distorting effect of added pressures. The distortion essentially consists of a broadening of the spectral response plots and a shifting of the resonance peaks/dips that are present in all the graphs of the effective moduli and/or the effective acoustic/material properties of the pertinent composites. For the lossy, air‐filled, rubberlike materials considered here, the pressure effect seems to be quite noticeable, but smaller than the viscous effect or than that of the nonuniformity in the cavity‐size distribution functions. The model is implemented by a computer code and its numerical predictions are quantitatively displayed for a few of the effective properties of a given perforated elastomer up to pressures of 400 psi. These are the pressures present down to ocean depths of about 900 ft. These perforated elastomers have uses as underwater sound absorbers.