The main objective of this paper is to classify rainfall radar images by using the scattering transform, which gives us a translation invariant representation of the images and preserves high-frequency information useful to encode important morphological aspects of the meteorological phenomena under study. To demonstrate the usefulness of the approach, a classification framework is considered, where the images are to be classified into 4 morphological classes: light rain, shower, unorganised storm and organised storm. Experiments show that the benefits of the scattering are threefold: 1) it provides complementary information with respect to more traditional features computed over the distribution of the rainfall intensities, 2) it provides strong invariance to deformations, 3) second order coefficients of the scattering transform nicely encodes spatial distribution of rain intensity.