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Lava tubes are buried channels that transport thermally insulated lava. Nowadays, lava tubes on the Moon are believed to be empty and thus indicated as potential habitats for humankind. In recent years, several studies investigated possible lava tube locations, considering the gravity anomaly distribution and surficial volcanic features. This article proposes a novel and unsupervised method to map candidate buried empty lava tubes in radar sounder data (radargrams) and extract their physical properties. The approach relies on a model that describes the geometrical and electromagnetic (EM) properties of lava tubes in radargrams. According to this model, reflections in radargrams are automatically detected and analyzed with a fuzzy system to identify those associated with lava tube boundaries and reject the others. The fuzzy rules consider the EM and geometrical properties of lava tubes, and thus, their appearance in radargrams. The proposed method can address the complex task of identifying candidate lava tubes on a large number of radargrams in an automatic, fast, and objective way. The final decision on candidate lava tubes should be taken in postprocessing by expert planetologists. The proposed method is tested on both a real and a simulated data set of radargrams acquired on the Moon by the Lunar Radar Sounder (LRS). Identified candidate lava tubes are processed to extract geometrical parameters, such as the depth and the thickness of the crust (roof).