The method of calculating the effective deformation diagrams for incompressible laminated composites with finite deformations are suggested. The method is based on the application of the theory of asymptotic expansions over small geometrical parameters to a general non-linear elasticity equations with finite deformations of inhomogeneous media with a periodic structure. It was used suggested earlier the universal representation of constitutive relations for nonlinear elastic compressible media with finite deformations. A solution of the local problems over the periodicity cell in a formal explicit form of interconnected systems of nonlinear algebraic equations was received. It was mathematically rigorously proved that if the phase of the composite are incompressible, the composite as a whole is also an incompressible material. The example of numerical calculation of the effective deformation diagrams multilayer composite fibers are described by the model of nonlinear elastic incompressible material such as Money.