The amount of radar sounder data, which are used to analyze the subsurface of icy environments (e.g., Poles of Earth and Mars), is dramatically increasing from both airborne campaigns at the ice sheets and satellite missions on other planetary bodies. However, the main approach to the investigation of such data is by visual interpretation, which is subjective and time consuming. Moreover, the few available automatic techniques have been developed for analyzing highly reflective subsurface targets, e.g., ice layers, basal interface. Besides the high reflective targets, glaciologists have also shown great interest in the analysis of non-reflective targets, such as the echo-free zone in ice sheets, and the reflective free zone in the subsurface of the South Pole of Mars. However, in the literature, there is no dedicated automatic technique for the analysis of non-reflective targets. To address this limitation, we propose an automatic classification technique for the identification of non-reflective targets in radar sounder data. The method is made up of two steps, i.e., i) feature extraction, which is the core of the method, and ii) automatic classification of subsurface targets. We initially prove that the commonly employed features for the analysis of the radar signal (e.g., statistical and texture based features) are ineffective for the identification of non-reflective targets. Thus, for feature extraction, we propose to exploit structural information based on the morphological closing profile. We show the effectiveness of such features in discriminating of non-reflective target from the other ice subsurface targets. In the second step, a random forest classifier is used to perform the automatic classification. Our experimental results, conducted using two data sets from Central Antarctica and South Pole of Mars, point out the effectiveness of the proposed technique for the accurate identification of non-reflective targets.