In a method and a device for machining an elongate workpiece that is not rotationally symmetrical in the form of turbine blades, the workpiece is supported by a steady rest that has clamping elements for clamping the workpiece on the cross-section thereof that is not rotationally symmetrical. After clamping the workpiece, the steady rest moves with its open clamping elements along the longitudinal axis of the workpiece into a supporting position. During movement of the steady rest into the supporting position and/or while the supporting position of the steady rest is being changed, a collision between the open clamping elements of the steady rest and the workpiece is prevented by a program-controlled rotation of a rotary part of the steady rest.