High density cellulose-based materials have been widely used for electrical insulation and (interior) construction or structural material. Similar to typical paper/board materials, the microstructure of high-density fibre mats consists of a porous network of cellulose fibres, which contributes to its highly non-linear mechanical response. Such fibre mats exhibit strong anisotropic material behaviour as well as significant transient (time-or rate-dependent) behaviour. The present investigation is aimed at studying the transient behaviour of high-density cellulose fibre mats, particularly during out-of-plane compression. A viscoelastic-viscoplastic constitutive model dedicated for high-density cellulose-based materials has been used to simulate the responses of the high-density cellulose-based fibre mats upon two types of transient loading, i.e. compressive creep and stress relaxation. The predictions of the model are then compared to the corresponding experimental characterization results, which indicate that material densification mechanism plays a more critical role during out-of-plane compression creep than in stress relaxation.