A study has been made of the isothermal, pressure-induced flow of liquid helium II through glass capillaries of bore between 2.6 × 10^-3 and 4 × 10^-2 cm. The critical velocity is found to be less than 1 cm. sec^-1 except, possibly, in the case of the finest capillary. The theory that there is a force of mutual friction between the normal and superfluid components predicts the correct order of magnitude for the flow velocities, but there are discrepancies which suggest the existence of some other source of friction.