A highly-tight screw joint comprising internal and external mating elements with conical surfaces used in connection with oil and gas wells. The internal and external elements are provided with a thread with supporting and embedded faces. A sealing unit is made in the form of a wedge on the side of a small diameter. The sealing unit is provided on the internal and external elements and consists of parts of the internal and external elements. The internal and external elements are formed by conical radial and conical supporting faces. The conical radial face is made at an angle of 25°-35° to the normal to the thread axis. The conical supporting surface is made at the angle of 10°-25° to the normal to thread axis.