The pack has a receiving compartment provided for a hydrophilic medical instrument e.g. lancing device, for insertion into a body tissue. The pack exhibits a specific proportion of volatile constituents after the radiation sterilization. The hydrophilic medical instrument is provided with a hydrophilic coating sectionally, and the pack is made of plastic e.g. polyester. The pack exhibits a wall thickness between 1 and 500 meter. An inner layer of pack exhibits a polyester layer, where the pack encloses a test unit for application with body fluid.
