In recent years, the use of timber as a building material in larger construction applications such as multi-story buildings and bridges has increased. This requires a better understanding of the material to realize such constructions and design them more economically. However, accurate computational simulations of timber structures are challenging due to the complexity and inhomogeneity of this naturally grown material. It exhibits growth inhomogeneities such as knots and fiber deviations, orthotropic material behavior and moisture dependence of almost all physical parameters. Describing the creep response of wood under real climate conditions is particularly difficult. Changes in moisture content, plasticity and viscoelasticity affect moisture-induced stresses and potentially lead to cracks and structural damage. In this paper, we apply a material model that combines time and moisture-dependent behavior with multisurface plasticity to simulate cross-sections of different dimensions over a 14-month climate period. Our findings indicate that considering this long-term behavior has a minor impact on moisture-induced stresses during the drying period. However, during the wetting period, a purely linear elastic description of the material behavior of wood significantly overestimates tensile stresses within the cross-section, resulting in unrealistic predictions of wetting-induced fracture. Therefore, simulations during wetting periods require a sophisticated rheological model to properly reproduce the stress field.