A thermal material-processing method wherein between the working spot of an electron beam and a workpiece a relative motion is brought about. Prior to the actual thermal treatment an effective processing contour is ascertained, in that the working spot of the electron beam executes, in accordance with the stored data of an ideal processing contour, a relative motion in relation to the workpiece, and on this relative motion a scan motion is superimposed which is directed transversely to the ideal processing contour. In this manner, both geometrical and magnetically conditioned deviations of the points of incidence of the electron beam on the workpiece can be compensated.