Special configurations of gaskets are used in hydro systems working at extremely high pressures. The present article deals with such a movable cylindrical gasket that comprises a body – thick-walled tube and a cover –thin- walled tube in the gasket area. Relations are derived concerning the inner stress state of the thick-walled tube depending on the outer diameter of the tube facilitating the choice of the latter. The alterations of the values of the stresses in the contact surface, the body and the cover are examined using the Finite Elements Method (FEM). Some constructive suggestions are presented in the article that will lower the values of the contact stresses in the cylindrical gasket.