Precision glass tubes for analytical instrumentation often require tight tolerances in their inner and outer diameter, which makes them cumbersome to fabricate. The extrusion method is a potential method for the fabrication of precision glass tubes, however, the effects of die swell and taper which occur during the extrusion process can distort the final product. This work aims to determine the tolerances that can be achieved for glass tubes fabricated using the extrusion method by comparing the extent of the die swell and tapering on tubes extruded under a variety of extrusion parameters. Lead‐silicate glass tubes of 6.5 mm outer diameter and 0.50 mm inner diameter were fabricated with a taper of <1% for the outer diameter and <5% for the inner diameter over 200 mm lengths. This target geometry was achieved using a volume flow rate of 4.7 mm3/s, a glass viscosity of 107.2 Pa.s and a die geometry that accommodated a 8%‐10% offset due to die swell. This result indicates the extrusion method is a viable method for producing glass tubes with tight tolerances for applications in analytical instrumentation.