A process and a device for grinding, especially edge grinding, of elongated objects (15), the device consisting of a basic frame (1) which supports a carriage (13) horizontally displaceable by means of a first pulse motor (23) and a scanning member or a grinding wheel (18) vertically displaceable by means of a second pulse motor (25) and where the carriage (13) is equipped with members for clamping of the object (15) to be ground, and where the carriage (13) is directly connected to members (27) for observation when the scanning member in a vertical movement comes into contact with the object (15) to be ground. The process comprises as a first step scanning of an existent profile of the object (15) to be ground, whereunder alternately (a) the carriage (13) is displaced over a little distance and (b) the scanning member is diplaced to contact with the object (15) to be ground, which values are recorded and treated in a connected computer (7) to be utilized thereafter in a second step for control of the grinding wheel (18) which thereunder exactly imitates the scanned and computed values.