A sealing device for sealing at least two facing surfaces of two adjacent machine elements includes an inflatable sealing tube arranged in a groove in a first surface of a first machine element. The sealing tube can be filled with a medium to which pressure can be applied, and can be inflated by the medium as well as made to rest against a second surface of a second machine element, forming a seal. The ends of the sealing tube are each arranged in an insert piece. The insert pieces are each structured as a sleeve and surround the ends of the sealing tube under elastic pre-stress, forming a seal. The sleeves are each arranged in a recess of the first machine element that extends essentially crosswise to the lengthwise direction of the groove. In the non-pressurized state, the sealing tube and the face of the sleeves that faces the second surface of the second machine element are essentially flush with the first surface of the first machine element.