Cellulose-based components constitute the bulk of the current insulation for transformers. Cellulose is an organic polymer material which combines excellent electrical properties and good mechanical performance. As a polymeric material, cellulose is very sensitive to moisture and temperature. These factors can influence the electrical and mechanical performance of a transformer throughout its lifetime. In order to ensure the quality of the product during transformer manufacturing, as well as during transformer life-time services, adequate models for predicting the physical properties of its constituents are needed. The present investigation tackles the mechanical description of pressboard. For this purpose, a three dimensional mechanical model is developed for simulating the in-plane and out-of-plane behavior of the pressboard material. The model is based on an anisotropic viscoelastic-viscoplastic constitutive law, which includes features that are particular for cellulose-based materials, e.g. the peculiar double nature of fiber-network-based and porous material. The material is orthotropic by nature, i.e. the in-plane mechanical properties markedly differ from the out-of-plane ones. Particular regard is taken when considering the effect of out-of-plane stresses which both cause viscous deformation and permanent compaction. The analyses on the mechanical behavior of pressboard are performed by comparing the experimental data on pressboard and the results of model simulations.