To provide an infeed form rolling die with which working of a screw shaft in which the balls are prevented from falling off is easily performed and the screw shaft of a ball screw mechanism which is formed with the die.

The balls 3 can pass through smoothly because the cross-sectional shape of a passage of a male screw groove 1a is lager than the cross-sectional shape of the ball 3, but the cross-sectional shape of the passage of a dummy male screw groove 1a' is smaller than the cross-sectional shape of the ball 3 and the ball 3 is stopped to pass through by the fact that the portions showed by double cross hatching are hit. That is, the balls 3 are prevented from falling off by providing the dummy male screw groove 1a'.