Mechanical surface hardening processes have long been of interest to science and technology. Today, surface modification technologies have reached a new level. One of them is friction stir processing that refines the grain structure of the material to a submicrocrystalline state. Previously, the severe plastic deformation occurring during processing was mainly described from the standpoint of temperature and deformation, because the process is primarily thermomechanical. Modeling of friction stir welding and processing predicted well the heat generation in a quasi-liquid medium. However, the friction stir process takes place in the solid phase, and therefore the mass transfer issues remained unresolved. The present work develops the concept of adhesive-cohesive mass transfer during which the rotating tool entrains the material due to adhesion, builds up a transfer layer due to cohesion, and then leaves it behind. Thus, the transfer layer thickness is a clear criterion for the mass transfer effectiveness. Here we investigate the effect of the load on the transfer layer and analyze it from the viewpoint of the friction coefficient and heat generation. It is shown that the transfer layer thickness increases with increasing load, reaches a maximum, and then decreases. In so doing, the average moment on the tool and the temperature constantly grow, while the friction coefficient decreases. This means that the mass transfer cannot be fully described in terms of temperature and strain. The given load dependence of the transfer layer thickness is explained by an increase in the cohesion forces with increasing load, and then by a decrease in cohesion due to material overheating. The maximum transfer layer thickness is equal to the feed to rotation rate ratio and is observed at the axial load that causes a stress close to the yield point of the material. Additional plasticization of the material resulting from the acoustoplastic effect induced by ultrasonic treatment slightly reduces the transfer layer thickness, but has almost no effect on the moment, friction coefficient, and temperature. The surface roughness of the processed material is found to have a similar load dependence.