A fastening system for medical devices includes a column-shaped interface profile (1) having a lens-shaped cross section with at least one convexly shaped, longer front surface (2) and with two shorter lateral surfaces (3), which are parallel to one another and pass over into the longer front surface (2) via a tappet-shaped projection (4) each. A clamping device (6), fits the longer front surface (2) of the interface profile (1) with the two tappet-shaped projections (4) in a positive-locking manner for fastening medical devices. The clamping device (6) has a concavely shaped outer surface and is provided with clamping jaws (8) that can be set on one side or on both sides for detachable fixation on the interface profile (1). This construction offers the possibility of receiving medical devices and accessories on up to a maximum of four sides simultaneously, especially also via standardized rail elements (7).