The sapwood fibers in green softwood are normally filled - or nearly filled - with free water. This water forms a continuous phase through the narrow bordered pits between fiber lumens. In a drying process water evaporates from the menisci formed at these narrow throats and initially located close to the surface of the wood. As the amount of free water decreases in this way, a retraction of the meniscus will happen in the widest throat, which can be located anywhere, not necessarily close to the surface. As the individual size of these narrow throats is a stochastic variable, this process will produce complicated water phase structures that gradually fragmentize. If this drying behavior is viewed as such an invasion percolation process it is obvious that the result differs from normal diffusion, which however most often is used as the basis for wood drying modeling. A computer based simulation model that utilizes the above principle has been developed. This model has been used for the simulation of a few situations of practical and theoretical importance. It has been found that this invasion percolation approach can reproduce some previously unexplained features seen in softwood drying processes. Some detailed examples are presented in this paper