It faces southwest, and rises about 200–300 m.[1] It is located in the northeastern portion of the Mare Tranquillitatis, and is named after the nearby crater Cauchy.
The east end of Rupes Cauchy emerges from the highlands on the eastern margin of Mare Tranquillitatis.
At the west end of the Rupes are two similar-sized elongate depressions (unlikely to be impact craters).
Between Cauchy B and the depressions the Rupes form an en echelon pattern, similar to that of veins within rock on earth, on a grand scale.
[2] Rupes Cauchy casts a thin shadow about five days after the new moon, when the sunrise terminator is nearby and the sunlight is arriving at a low angle.