A method of removing a predetermined amount of abrasive material from the internal surface (16, 18, 20, 22) of an article (10) whose profile deviates from a perfectly circular configuration. The external surface (32) of the article (10) is probed by contact in order to determine its true location in space, the data then being compared with the engineering data to delimit the location of the surface ( 16, 18, 20, 22) where the material must be removed. A control computer (70) sends orders to a machine control system, the machine removing excess material to give the article the desired dimensions. Any deviation from the required circular configuration is compensated for by the radial displacement of the article (10) relative to the cutting tool, as the article (10) advances in the direction of the circumference relative to the cutting tool.
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