We study a deformation behavior of a composite with small volume content of fibers. The composite is reinforced in three mutually orthogonal directions. We consider the case of large shear deformations. We use the applied theory that allows us perform the macro-mechanical analysis of composite materials with small volume content of fibers and obtain results valuable for applications. We consider the qualitative difference between three-orthogonally reinforced composites under large deformations and these composites under small deformations. We study the phenomenon of macroscopic loss of stability of the composites considered under large shear deformations contrary to the case of three-dimensional composites with large volume content of reinforcing fibers.