It is now widely accepted that the contact between two surfaces is in fact a one-to-one contact between many asperities, depending on the roughness of the contact pair. This represents a strong deviation from the perfect contact assumed in engineering approaches, with the real contact area being significantly smaller than the apparent contact area.In addition, such an approach also implies the presence of a free space between surfaces in contact. Thus, the purpose of our study is the development of numerical tools to analyse the mechanical contact between rough surfaces and the tightness of such a contact.Two different approches are studied. The first one is devoted to the observation of the mechanical contact between a rough surface and a rigid plane by means of the finite element method and a new numerical model. The second approach is related to the estimation of the contact transmissivity by considering simulations of the fluid flow in the resulting free space between surfaces in contact.The comparison between experimental and numerical estimations of the resulting flow rate shows significant deviations.In order to understand these deviations, the influence of material models on contact simulations is studied. In particular, the effect of using crystal plasticity and the effect of including plasticity-driven temperature changes are considered. The question of problem representation in fluid flow approaches is also addressed.