We consider the problem in Synthetic Aperture RADAR (SAR) of identifying and classifying objects located on the ground by means of Convolutional Neural Networks (CNNs). Specifically, we adopt a single scattering approximation to classify the shape of the object using both simulated SAR data and reconstructed images from this data, and we compare the success of these approaches. We then identify ice types in real SAR imagery from the satellite Sentinel-1. In both experiments we achieve a promising high classification accuracy ($\geq$75\%). Our results demonstrate the effectiveness of CNNs in using SAR data for both geometric and environmental classification tasks. Our investigation also explores the effect of SAR data acquisition at different antenna heights on our ability to classify objects successfully.