In a method for producing free curved surfaces for cutting a workpiece (3) into a free curved surface contour on the basis of a free curved surface data representing the contour of a free curved surface, when a tool (5) is caused to approach the starting point of machining for target contour (SC) on the workpiece, the moving direction of the tool reaching the starting point of machining is determined such that it substantially coincides the tool's starting direction for machining whereby an approach path is provided through which an excessive cutting is avoided at the starting point of machining, and such approach path is corrected on the basis of a tool path that has been prepared correspondingly to the cutting target contour (SC) on the workpiece so as not to cause a tool interference whereby an approach path of the tool (5) may be achieved through which an excessive cutting is avoided at the starting point of machining and a tool interference does not occur.