Surface growth of solids includes a wide variety of processes starting from additive manufacturing technologies and ending with plenty of biological problems. Model of surface growth based on the expression of the configurational force, derived from fundamental laws and entropy inequality, is offered in the present paper. A new expression for the configurational force called surface growth force, which controls growth and resorption, is used. Analysis of the applicability of the developed model was carried out for problems of surface growth of compressed cylinder with prestrained growth layer and growth layer without prestrain. The influence of matter supply function and mechanical stresses as one of the main process controlling factors on the surface growth was also investigated.