A transient two-dimensional mathematical model is developed to simulate the through-air drying process for tufted textile materials. The heat and mass transfer in a cylindrical porous medium and the air flowing around it are analyzed separately. First, thermal and mass circuits are used to analyze the simultaneous heat and mass transfer within the porous medium. Then, the equations of the conservation of mass and energy are written for the drying medium. The resulting system of three non-linear differential equations is numerically solved by an implicit finite difference method. The numerical solutions are compared with experimental drying results obtained using magnetic resonance imaging (MRI) and a laboratory through-air dryer (LTAD).