Environmental impact assessments for seismic surveys often include estimates of radially propagating sound levels, which are used to determine marine mammal impact zones. Sound levels may be estimated using computer-based acoustic modelling techniques but these require an accurate description of the survey source signature—arrays of airguns, in particular, have complex, highly directional source functions that depend on the array layout. To address this requirement, an airgun array source signature model has been developed for the purpose of underwater noise level prediction. The source model is based on published descriptions of the physics of airgun bubble oscillations and radiation [A. Ziolkowski, Geophys. J. R. Astron. Soc. 21, 137–161 (1970)] and includes the effects of port throttling, motion damping and bubble interactions. The output of the model is a collection of notional signatures which may be used to compute the source function of the array in any direction. Free parameters in the model have been fit to a large collection of existing airgun signature data, for airguns ranging from 5 to 185 in3. The output of the model is suitable for estimating sound levels resulting from airgun survey activity. [Work supported by NSERC.]