The quantum-mechanical approach (the density functional theory and the pseudopotential method) is used to study the friction in the nanopairs “aluminium – aluminium”, “aluminium – tungsten” and “tungsten – tungsten” on the atomic level; an external pressure was taken into account. Nanopairs were constructed from crystalline nanoslabs and crystalline nanorods with rectangular cross sections. Nanoslabs had infinite periodic structures along X and Y directions; nanorods were periodic in the Y directions. Process of friction was studied by reduction of a rod and a slab in equilibrium contact with the subsequent step-by-step shift of a rod concerning a slab along the X direction. During the process the rod was over a plate (in the direction of Z). The total energy of system was calculated on each step. The friction force was calculated as a relation of change of the total energy to the value of the rod shift step. Pressure force was applied to a rod on axis Z. The coefficient of friction was as the friction force relation to the pressure force. Observation over behavior of atoms showed that for all studied nanopairs process of friction is followed by processes of deformation and destruction. Thus deformations are subject both components of a nanopair, but destructions are observed only in a nanorod. Aluminium rods are subject to the maximum deformations and destructions: both in pairs “aluminium-aluminium”, and in pairs “aluminium-tungsten”. Tungsten rods do not destruct, and deformations in them and in tungsten plates are minimal. Friction coefficients for pairs “aluminium-aluminium” decrease with increasing of pressure, and they increase for “aluminium-tungsten” and “tungsten-tungsten” pairs.