A method of making a perforated tubular member by supporting a thin stainless tube (10) on a mandrel; machine engraving funnel-shaped holes ( 12 ) through the tube ( 10 ) and removing the machine-engraved tube from the mandrel. An alternate embodiment applies an intermediate layer (22) of aluminum to a core roll (20); applies a plurality of metallic layers (24) to the intermediate layer (22); machine engraves funnel-shaped holes (12) through the metallic layers (24); etches away the intermediate layers (22) and removes the machine-engraved tube. A third embodiment applies a separating-chemical layer (32) to a core roll (30); electro plates a plurality of metallic layers (34); machine engraves funnel-shaped holes (12); into the metallic layers ( 34 ); releases the resulting tube from the separating layer (32); and removes the resulting tube from the core roll.