Abstract: The present invention is a control method and numerical control for the vibration-reduced acceleration of a movable machine element of a numerically controlled industrial processing machine, in which a path of movement of the machine or machine element is broken down into directly successive interpolatable movement sections In the interpolation, resultant acceleration profiles which lie in a range close to a critical natural frequency of the machine or machine element are carried out with a reduced acceleration. By this method, intervention is made only in critical ranges of the acceleration profile, uncritical ranges remain uninfluenced, as a result of which drastic time losses during positioning can be avoided.