Abstract A physical model for acoustic scattering by fish aggregations is developed. This differs from earlier models in not being a formal derivative of reverberation theory. No specific assumptions are made about the effects of individual fish on transforming the incident signal waveform, the effect of fish behaviour, or sonar beam patterns. General expressions for the mean and variance of energy contained in received echoes are derived. These are applicable to the output of fish echo integrators in the noise-free limit. The expressions are reduced for the important case of independent fish behaviour. As an example, the coefficient of variation of echo energy from Poisson-distributed fish in a horizontal layer is computed under the point scatterer assumption. Some potential uses of the model are indicated.