The machine is for the decorative grinding of hollow glasses, vases etc., having a grinder head swinging in a horizontal plane and with a rotary disc, also a holder securing the glass with its axis at right angles to that of the slewing axis. The holder slides in relation to the grinder disc in the axial direction of the glass, and also turns about the glass axis and can be tilted and lifted in relation to the disc. Independent drive units are programmed to take account of the glass shape, disc diameter, and grinding pattern and speed, so as to impart the necessary movements to the head and holder. The glass-holder (5) is mounted on one side (11) of a parallelogram guide (10) working in a vertical plane. The side of the guide (12) opposite the holder pivots about an axis (19) at right angles to this plane. The holder is mounted close to the first side (11).
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