PURPOSE: To enable production of highly precise and efficient curve without generation of navel by constituting so that a cutting tool is given rotation at the time of cutting of rotating center area of common end face at least in curved surface machining method.

CONSTITUTION: In a curved surface machining method in which a curved surface is formed on a material to be machined with cutting machining, a cylindrical material to be machined 1 is held to a chuck 8. And a first and a second main shafts 7, 14 are rotated and the material to be machined 1 is rotated to the direction of an arrow 9 and a cutting tool 3 is rotated to the direction of an arrow 17. Then a rotating mechanism 12 and a feed mechanism 10 start to operate based on the instruction from a numerical control unit 5, and the cutting tool 3 begins cutting of an end face of the material 1. This time, a cross angle θ of an axial lines 7a and 14a is numerically controlled so that inclined angles λ1, λ2... made by contact faces 26... in machining points 25... on a cutting line face 24 and the tool 3 become almost constant. Thus, production of curve can be made in high precision and efficiency.