Wood is a natural engineering material that has traditionally been exploited in design for a wide variety of applications. The recent demand for sustainable material and construction processes in the construction industry has triggered a renewed interest and research in the inherent properties of wood and their derived applications, and specifically for developing low-tech architectural adaptive systems. This paper focuses on the physical and computational modeling of the morphing behavior of wood through hygroscopic expansion or contraction to a high degree of precision. The amount of stress related to the hygroscopic shrinking or swelling ranges from almost zero to high values, and its prediction is fundamental to alleviate any fatigue challenges. The capability of designing wood composite whose stress state remains limited under changes of the environmental humidity is beneficial for any engineering application subjected to a repeated reversal of loading such as adaptive systems. In this paper, a mechanical model, together with its numerical implementation, is presented; the model is benchmarked against some prototypical experiments, performed by using real material parameters. The control parameter in the model is the relative moisture change in wood that determines the orthotropic swelling/de-swelling phenomenon, and is coupled with the elastic behavior of wood. This model is integrated into a programmable matter design approach that combines physical and computational exploration. The approach is illustrated for a hygro-morphic building façade panel. The approaches and algorithms presented in this paper have further applications for computer-aided design of smart materials and systems with interchanging functionalities.