A METHOD OF PRODUCING GLASS CAPS OF NON-CIRCULAR CROSS-SECTION BY FIRST FORMING A GLASS TUBE OF THE DESIRED NON-CIRCULAR CROSS-SECTION AND THEN HEATING A RESTRICTED PERIPHERAL ZONE OF SAID GLASS TUBE, WHILE THE SAME IS NONROTATABLY SUPPORTED, BY FLAMES FROM A PLURALITY OF NOZZLES OF A STATIONARY BURNER SUBSTANTIALLY SURROUNDING SAID GLASS TUBE AT SAID PERIPHERAL ZONE, SAID NOZZLES BEING SO DIMENSIONED AND SO ARRANGED TO PRODUCE EQUAL HEATING CONDITIONS ALONG SAID ENTIRE NON-CIRCULAR PERIPHERAL ZONE, WHEREBY UPON REMOVAL OF THE LOWERMOST SUPERFLUOUS MATERIAL FROM THE GLASS TUBE A BOTTOM IS FORMED ON THE CAP.