In a spinning machine for shaping a blank into a product of a desired configuration without using a metal mold, there are provided a rotary shaft, a push rod, the rotary shaft and push rod cooperating to clamp therebetween a flat plate shaped blank for rotating the same, a back-up roller having a peripheral contour conforming to a portion of the inside contour of a spinned product, means to urge the back-up roller against one side of the blank, means to move the back-up roller along a predetermined path conforming to the inside contour of the product, a work roll having a working edge of smaller radius of curvature than said back-up roller, means to urge the work roll against the opposite side of the blank with a predtermined definite axial spacing between the work roll and the back-up roller and means for moving the work roll to follow the movement of the back-up roller while maintaining the definite axial spacing with respect to the back-up roller.