A medical device for shutting off a body channel is provided including a band section that can be placed around the body tissue surrounding a body channel and can be closed to form a ring enclosing a passage opening for the body tissue, and has a cavity which makes up one part of a working fluid receiving chamber of the device, for receiving working fluid, and a pump unit for conveying the working fluid. The passage opening is made smaller by introducing the working fluid into the cavity. The arrangement also includes a storage container that has a flexible wall which delimits a storage chamber, wherein to apply an additional force to the body tissue guided through the passage opening, the volume of the storage chamber is made smaller by increasing an ambient pressure acting on the storage container, and the wall of the storage container is at least substantially non-extensible.
