Various processes are associated with the surface growth of solids, such as biological growth, formation of surfaces, processes accompanying additive technologies. Experiments show that the growth process of living and non-living matter can be controlled by external influences, including mechanical ones. This paper presents a surface growth model based on the expression for the configurational force obtained from the fundamental balances of mass, momentum and energy, and the second law of thermodynamics in the form of the Clausius-Duhem inequality. It is shown that the configurational force is the normal component of the tensor, called the surface growth tensor, which controls the processes of growth and adaptation to external mechanical loads. A kinetic equation in the form of the dependence of the growth rate on the growth tensor is formulated. A solid body is considered, in which a volumetric supply and subsequent diffusion of matter to the growth boundary occur. On the surface of the body, the transformation of one substance into another occurs, resulting in surface growth or resorption of the body. The surface growth process depends on the stress-strain state of the body and the concentration of the diffusing matter. In the process of growth, stresses and deformations change, affecting the configurational force and the rate of the matter supply, which also affects the configurational force. In addition, the model takes into account the growth strains that can occur in new layers of the material and affect the growth velocity. Thus, there is a coupled problem including the description of the supply, diffusion and growth processes and determination of the stress-strain state. The model was used for the problems of surface growth of various bodies under various loading conditions.