Abstract: Method of grinding elongated, cylindrical workpieces in continuous operat in a grinding machine wherein the workpieces are advanced while they are rotated about their longitudinal axes includes exerting an oscillating grinding pressure transversely to the longitudinal axis of the workpiece, and adjusting the frequency of the oscillations to lie substantially in low-to-medium frequency range, outside the frequency ranges of resonant vibrations of parts of the workpiece and of the grinding machine; and device for carrying out the foregoing method.