Three types of mathematical models (a single board-drying model, a kiln-wide drying model and a drying stress model) have been developed for the simulation of kiln drying of softwood lumber and the simulation of drying stresses. The single board-drying model employs comprehensive heat and moisture mass transfer knowledge and considers the influence of wood physical characteristics and moisture state. The model is used to investigate the influence of lumber variability such as wood density, green moisture content, growth ring pattern, mixture of sapwood and heartwood and thickness variation. The kiln-wide drying model, which was developed for the simulation of the drying of a kiln wide stack, is based on the transfer processes between the wood material and the drying medium. This model is able to examine the influence of varying wood properties and drying schedules on drying rate and moisture content distribution between boards. The stress model has been proposed to predict stress development in drying, and stress relief in final steam conditioning and post-kiln treatment. The stress model considers wood shrinkage, stress-strain relationships, mechano-sorptive behavior, creep and temperature effect. It is found that the rheological properties of wood play an important role in drying stress relief. The stress model is used to optimize drying schedules and to effectively relieve the residual drying stresses.