A theory of external reverberation in urban built-up environments is developed, based on a classical room acoustical model. In the model, external reverberation is analyzed as a special limiting case of internal reverberation in rooms. Explicit formulae are deduced for the statistical value of the external reverberation time, and the spatial distribution of the external sound field amplitude with distance from a fixed, constant power, sound source, for which comparison with published experimental results is possible. Predictions of the theory compare reasonably well with the experimental values. It is found that the external reverberation time in a built-up area depends chiefly on the average building height, and to a lesser extent on the packing fraction, and the ratio of surface area to cross-sectional area of buildings which make up the built-up environment, apart from the absorptive properties of the building and ground plane surfaces. For the spatial distribution of the steady state sound field amplitude in a built-up environment, it is found that the diffuse field amplitude attenuates with distance from a fixed, constant power source exponentially faster than the inverse square law.