Grooved tubing having a groove in the outer sidewall and a hole through the bottom of the groove is made by extruding a first plastic to produce a molten tubular extrudate, extruding a second plastic in the exterior of the sidewall of the tubular extrudate, subsequently removing the second plastic to provide a groove in the tubular extrudate and forming an opening through the bottom of the groove. This method can be used in making suction catheters wherein the groove walls prevent invagination of body tissue into the hole in the groove during suctioning.