We interpret cooperative scattering by a collection of cold atoms as a multiple-scattering process. Starting from microscopic equations describing the response of N atoms to a probe light beam, we represent the total scattered field as an infinite series of multiple-scattering events. As an application of the method, we obtain analytical expressions of the coherent intensity in the double-scattering approximation for Gaussian density profiles. In particular, we quantify the contributions of coherent backward and forward scattering.