A mathematical model for simulation of softwood drying also in temperatures exceeding the boiling point of water is presented. The equations are formulated in a conservative form based on the classical volume averaging technique with an addition of a pressure-driven moisture flux in the boundary condition. Numerical results using the control volume method are presented to show that this term missing in existing simulation models may account far the calculated build up of moisture at the very surface of a wood board. The possibility of neglecting the air- phase in the calculation of total gaseous pressure is investigated by means of an example. It shows that the effect of air pressure is only of very litde importance in the case of transversal flow in moderate tempertures.