The sea level rise determined by the continuous increase in the global temperature calls for a quantitative investigation of the continental ice subsurface features and their dynamics. In the past decades, the study of these features has been carried out by manually analyzing radargrams acquired by airborne-mounted radar sounder (RS) instruments at the Earth polar caps. As RSs provide a very large amount of data, the main challenge to an exhaustive analysis of the ice subsurface is the efficient extraction of useful information contained in radargrams. To address this challenge, in this paper we propose an automatic classification system of the main ice subsurface features visible in radargrams, i.e., ice layered area, bedrock scattering area and noise regions. The system relies on the extraction of a set of discriminant features which are computed on the bases of a detailed analysis of the statistical properties of the radar signal and of the spatial distribution of the subsurface features. The features are then given as input to a machine learning classifier based on Support Vector Machine (SVM). The proposed system is validated on a dataset made up of several radargrams acquired by an airborne RS in Antarctica.