Detection and characterization of avalanches are important for making avalanche inventories as well as for the management of emergency situations. In this paper we propose a scheme for automatic detection and mapping of avalanches in SAR images. The approach builds upon the hypothesis that compacted rough snow of an avalanche has very high backscatter intensity values compared to homogeneous snow cover and bare ground, and hence, by comparing the event image with a reference image we may detect and map avalanches in the scene. The proposed approach consists of two steps: (i) an initial detection of potential avalanche objects and, (ii) supervised classification of avalanche candidates using a random forest classifier. The approach is evaluated on a set of Radarsat-2 ultra-fine images, and the out-of-bag error rate is 6.4%. We conclude that an operational automatic algorithm may be feasible provided enough training data is available.