The microscopic response of a paper sheet to compressive forces is of great importance in predicting print quality as well as the sheet structures developed in wet pressing and calendering. In this report, we propose a new compression model that preserves the entire three-dimensional, stochastic, fibre network structure. The model includes Z-directional deformation of fibres in both compressive and shear modes. Permanent deformation of each fibre (such as caused by fibre collapse) can be achieved by adjusting the stiffness of the fibre during compression or unloading. The stiffness of the plates can also be chosen to represent, for example, a hard printing plate, a blanket, or a soft-nip calendar cover. Although we still need to collect basic fibre stiffness data in order to perform quantitative comparisons between model predictions and experimental results, simulated structures already show typical features of consolidated paper sheets. As a first application, we study the contact mechanics between a printing plate and a model paper structure.