The dimensional stability of printing paper is strongly related to changes in moisture content. This represents a major issue in the field of digital ink-jet printing, where moisture induced reversible and irreversible deformations may compromise printing quality and runnability. This paper proposes a two-dimensional hygro-mechanical model for paper, that focuses on the prediction of moisture induced out-of-plane deformations, due to inhomogeneous moisture variations in the plane. The model is based on a discrete network of beams. The adopted constitutive model, whose input parameters are calibrated to available experimental data for homogeneous moisture cycling, allows to describe typical irreversible phenomena related to the history of the production of paper, such as the release of dried-in strains. The deformation of paper in the wet and in the dry state predicted by the model is compared with experiments, in which the paper is subjected to a moisture cycle under different types of mechanical constraint. The results of the model capture well the experimental response of paper in terms of buckling patterns and of out-of-plane displacement wavelengths and amplitudes.