A method of joining a belt-tread assembly with a carcass assembly by stitching in tyre production using the device according to 1, in which pressure is applied in radial inward direction on an outer peripheral surface of a rotating belt-tread assembly connected with an inflated carcass assembly of a tyre, which is disposed on a tyre building drum, the pressure being exerted by said at least two stitching rollers which are rotationally and disposed on said device, wherein said device is provided with means for mutual symmetrical inelastic and axial movement of the stitching rollers from a central part of the outer peripheral surface of the belt-tread assembly of the tyre being produced to edges of the belt-tread assembly, and with said means for moving the stitching rollers along an axis perpendicular to the rotation axis A of the tyre being produced, characterised in that compressive force of the rollers being controlled by inelastic means for moving the said rigid bearing part in the direction of an axis perpendicular to the rotation axis of the tyre being produced with the proviso that the compressive force of the rollers is not induced by pneumatic cylinders.