In the present paper, the stress distribution in an infinite elastic body containing two neighboring nanofibers is studied. It is assumed that the midlines of the fibers are in the same plane. With respect to the location of the fibers according to each other the co-phase and anti-phase curving cases are considered. At infinity uniformly distributed normal forces act in the direction of the nanofibers, location. The investigations are carried out in the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrically non-linear exact equations of the theory of elasticity. The normal and shear self-equilibrated stresses arising as a result of the nanofiber curving are analyzed. In particular, the influence of the interaction between the fibers on the distribution of these stresses is studied. A lot of numerical results on the effect of the geometrical non-linearity to the values of the self balanced shear and normal stresses are presented.