Abstract: The engraving of an article with a curved surface is carried out at an order site. Engraving instructions are sent into computer equipment which controls an engraving machine by means of control signals which depend on the input instructions. The engraving machine comprises a rotatably arranged member in which the article is secured. The control signals are received in the engraving machine by control members which control the rotatable member and a device supporting an engraving tool. The rotatable member and the supporting device are controlled in coordination with each other in such a way that an engraving is obtained on the curved surface of the article.