A surface shape of a machining surface of a rotating elastic grindstone is rendered to be a shape appropriate to a to-be-machined surface of a work. With the work being rotated, the rotating elastic grindstone is held in engagement to an end of the to-be-machined surface of the work. The elastic grindstone is moved along a machining trajectory effective to allow the machining surface of the elastic grindstone, which is so formed as to suit to the to-be-machined surface, to follow the to-be-machined surface of the work. The to-be-machined surface of the work so superfinished represents a smooth surface free from any machining trace such as a crossing-angle pattern.