Within the framework of a piecewise homogeneous body model, with the use of exact equations of the three-dimensional geometrically nonlinear elasticity theory, the stress distributions in a unidirectional fibrous composite containing a row of periodically curved fibers is investigated. The midlines of the fibers are located in different parallel planes, and the curvatures of these lines are periodic and cophasal. The body is loaded at infinity by uniformly distributed normal forces in the direction of fiber location, and the stress distribution in it is investigated. The self-balanced normal and shear stresses arising as a result of fiber curvature are analyzed, and the effects of interaction between the fibers and of geometrical nonlinearity on their distribution are studied. The corresponding numerical results are presented and discussed.