In several works the normalized mechanical properties of composite materials with curved structures have been studied. These investigations have been carried out relying upon various approximate theories by employing different kinds of hypotheses. Furthermore, there are a few papers in which the above investigations have been carried out using the results obtained within the framework of the piecewise-homogeneous body model with the use of exact three-dimensional equations of linear theory of elasticity. However, under determination bf the normalized mechanical properties, these results do not enable one to take into account the nonlinear effects owing to the curvature of reinforcing layers of composite materials. Using a concrete problem as an example, the above method is developed for problems of stress-deformation distribution in such composite materials within a geometrically nonlinear framework and on the base of the obtained results, the nonlinear normalized mechanical properties of composite material with spatially periodically curved layers are determined.