Paper is a natural material, with an anisotropic structure composed of a network of cellulose fibers. This fibrous structure is highly sensitive to fluctuations in the moisture content. When paper is used in inkjet printing applications, it may experience significant deformations due to hygroexpansion. If the moisture content is not properly controlled, unacceptable deformations may result. In this work we implement a computational FE-based model to study the moisture transport and swelling in paper. Paper is modelled as a multi-phase material, using the hybrid mixture theory. This approach allows us to establish the balance equations for phases and constituents by rigorous averaging. Therefore, the constitutive laws and mechanisms driving the flow need to be defined at smaller scales, which allows a better correspondence with the underlying physics. In this framework, paper is considered as a two-phase system composed of fibers and inter fiber liquid. Within the fibers we consider two constituents: intra fiber liquid and dry fibers. Balance equations for phases and constituents are established to be consistent with the principles of thermodynamics, as described by Alexandersson and Ristinmaa (2018), where a triphasic model was derived to study porous cellulose networks. The novelty of the present work lies in the derivation of the constitutive models, which is motivated in fundamental principles of physics and assumptions at the microscale. We assume, for example, that the porous structure of paper can be represented as a partially saturated bundle of cylindrical pores. With this idea, we find a dependence between the permeability and the saturation of the tubes. The mechanical deformations were modelled by using an anisotropic hyper-elastic material model where we incorporate the fiber distribution of the paper sheet. The performance of the model is validated by using experimental data of plain paper.