Within the framework of the piecewise homogenous body model, with the use of the three-dimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for the determination of the stress distribution in the composites with unidirectional locally curved covered fibers is used for investigation of the shear stresses acting along the fibers. All the investigations are carried out for an infinite elastic body containing a single locally curved covered fiber, for the case where there exists the bond covering cylinder with constant thickness between fiber and matrix material are considered. It is assumed that the considered material is loaded at infinity by uniformly distributed normal forces in the fiber lying direction. Under formulation and mathematical solution of the boundary value problem, the boundary form perturbation method is used. The numerical results related to stress distribution in considered body and the influence of geometrical nonlinearity to this distribution are presented and interpreted.