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A fluid-mechanics model that make use of asymptotic analysis based on small aspect ratio of capillaries has been compared with the full 3-D set of the N.-St. equations, for modelling the fabrication of capillary tubes. The final asymptotic equations are solved numerically and then compared with the N.-St. solutions, obtained with a commercial finite elements solver. The present paper focuses on the comparison of the solution of the two methods taking into account the effects of surface tension and internal hole pressure, since those are of essential importance during drawing. It is shown that the analytical asymptotic method delivers reliable results for practical applications, as long as the inner pressure or the temperature does not exceed too high values.