A syringe assembly being assembled from a syringe for dispensing a dental or medical substance, and a protective cover. The protective cover has a geometrically determined, non-foldable tubular protective shaft. The syringe has a cartridge having an outlet for the substance. Further, the cartridge and the protective cover are assembled with the cartridge being received within the protective shaft. The syringe further comprises a dispensing tip that is connected to the outlet for dispensing the substance from the dispensing tip. A first seal is provided between the dispensing tip and the outlet, and a second seal is provided between the dispensing tip and the protective shaft.