Contrary to claims made in the recent literature, we show that the classical approach to mass transport in gas mixtures can be used to model two-dimensional Stefan tube diffusion. Numerical solutions are obtained for water evaporating into air, using the Kramers-Kistemaker diffusion slip velocity as the boundary condition on the side walls. A comparison is made with the analysis of Salcedo-Diaz et al. (2008 Velocity profiles and circulation in Stefan-diffusion. Chem. Eng. Sci. 63,4685-4693), in which the classical approach is rejected in favor of the Kerkhof-Geboers equations. Difficulties inherent in this latter approach are discussed in detail. (C) 2012 Elsevier Ltd. All rights reserved.