A method for producing a rubber member for ti res, by spirally winding an unvulcanized rubber strip, comprising the steps of: attaching the first longitudinal end portion of the rubber strip (s) to an substantially cylindrical object; spirally winding the rubber strip onto the cylindrical object; and attaching a second longitudinal end portion of the rubber strip to a wound assembly of the rubber strip formed in said winding step, wherein the each end surface of the first end portion and the second end portion has a front end edge extending, in plan view, from one side edge to another side edge of the rubber strip in the width direction thereof; the end surface of at least one of said first end portion and the second end portion is an inclined surface inclining to the longitudinal di recti on line of the rubber strip; said inclined surface is inclined to reduce thickness of the rubber strip gradually toward the front end edge; and the inclination angle θ of said inclined surface, in a cross section perpendicular to said front end edge, is in a range of 10 to 80 degrees with respect to the surface of the rubber strip including said front end edge, the method further compri si ng the step of pressi ng a cutting device against the rubber strip (s) to cut the rubber strip and to form said inclined surface on each end of cut portions of the rubber strip, the cutting device having a cutting edge extending in the width direction of the rubber strip and a pressing portion having a pressing face extending and inclined upward in the longitudinal direction of the rubber strip (s) from a root portion of the cutting edge; wherein the rubber strip (s) is cut on the cutting edge by pressing the cutting device against the rubber strip while the pressing face of the pressing portion presses the ends of the cut portions of the rubber strip to form the inclined surface on each of the ends, characterized in that the pressing portion constitutes a part of a circular column having an axis extending parallel to the cutting edge. attaching the first longitudinal end portion of the rubber strip (s) to an substantially cylindrical object; spirally winding the rubber strip onto the cylindrical object; and attaching a second longitudinal end portion of the rubber strip to a wound assembly of the rubber strip formed in said winding step, wherein the each end surface of the first end portion and the second end portion has a front end edge extending, in plan view, from one side edge to another side edge of the rubber strip in the width direction thereof; the end surface of at least one of said first end portion and the second end portion is an inclined surface inclining to the longitudinal di recti on line of the rubber strip; said inclined surface is inclined to reduce thickness of the rubber strip gradually toward the front end edge; and the inclination angle θ of said inclined surface, in a cross section perpendicular to said front end edge, is in a range of 10 to 80 degrees with respect to the surface of the rubber strip including said front end edge, the method further compri si ng the step of pressi ng a cutting device against the rubber strip (s) to cut the rubber strip and to form said inclined surface on each end of cut portions of the rubber strip, the cutting device having a cutting edge extending in the width direction of the rubber strip and a pressing portion having a pressing face extending and inclined upward in the longitudinal direction of the rubber strip (s) from a root portion of the cutting edge; wherein the rubber strip (s) is cut on the cutting edge by pressing the cutting device against the rubber strip while the pressing face of the pressing portion presses the ends of the cut portions of the rubber strip to form the inclined surface on each of the ends, characterized in that the pressing portion constitutes a part of a circular column having an axis extending parallel to the cutting edge.