A new model of swimbladder‐bearing fish has been developed in order to provide improved predictions of the resonance frequency and acoustic cross section of such a fish. The model consists of a small spherical shell in water, enclosing an air cavity which supports a surface tension. The shell is a viscous, heat‐conducting Newtonian fluid, with the physical properties of fish flesh. A comparison of the results obtained with the new model to experimental data indicates that the new model constitutes a definite improvement over previous models. The new model can predict the high values of damping and elevated resonance frequencies that previous models could not. The model appears to be most accurate for fish in which tension in the swimbladder wall has a minor effect on resonant scattering. This includes the fish which are of interest in studies of volume reverberation, and the new model should therefore be of considerable value in such studies.