A device for dispensing adhesive tape or for dispensing medical products stored on a roll, comprising a base plate, fitted with a pin upon which a roll or adhesive tape is attached, further a tearing section with a tearing blade spaced at a distance from the pin. The base plate is associated with a fastening section for partially gripping a rod, a bar or the like, wherein the fastening section comprises an arm connected to the base plate, merging with a crosspiece, which is fixed to a free arm such that the rod, bar or the like can be accommodated between the free arm and the connected arm, at least one fastening unit being provided to join the connected arm to the free arm.