The invention relates to a device for supporting medical instruments that are to be sterilized and/or cleaned, each comprising a fixing element, the support device comprising a plate having an underside face and a top-side face and in which there is formed at least one mounting through-hole (6) for a flexible retaining structure (7) for holding the element for fixing of a medical instrument, this flexible structure (7) comprising a system (8) of dismantleable connection to the plate. According to the invention, this flexible structure (7) comprises a top-side surface (71) that lies flush with the top-side face (51) of the plate (5) and in that the flexible structure (7) comprises an underside surface (72) lying flush with the underside face (52) of the plate (5).
