A syringe or carpule includes a cylinder that surrounds a cavity and comprises an end that has an access to the cavity, membrane seals the access and has a puncture area that can be punctured by a needle. A two-part cap has a predetermined breaking line and spans the membrane. A cover device covers the puncture area of the membrane in a sterile manner and comprises a sealing area spanning the puncture area. The sealing area covers the puncture area in a sterile manner regardless of axial forces to be applied in the area of the predetermined breaking line.