Exhaustive investigations of the ice sheet subsurface can be carried out by analyzing the information contained in the huge archives of radargrams acquired by dedicated radar sounder (RS) instruments. The analysis can be done by using properly designed automatic techniques for a quantitative, objective, and reliable extraction of information from radargrams. Unfortunately, the definition and development of such automatic techniques have only been marginally addressed in the literature. In this paper, we propose a novel and efficient system for the automatic classification of ice subsurface targets present in radargrams. The core of the system is represented by the extraction of a set of features for target discrimination. The features are based on both the specific statistical properties of the RS signal and the spatial distribution of the ice subsurface targets. Such features are then provided as input to an automatic classifier based on support vector machine. Experimental results obtained on two real-world data sets acquired by airborne-mounted RSs in large regions of Antarctica confirm the robustness and effectiveness of the proposed classification system.