Matrix composite materials reinforced with short axisymmetric fibers which elastic moduli are much larger than the moduli of the host medium are considered. The asymptotic solutions of the one-particle problems for a stiff fiber of various shapes are used in the framework of the effective field method for the calculation of the effective conductive tensors of the medium with fibers of large conductivity and the effective elastic stiffness tensors of the medium containing random sets of stiff axisymmetric fibers.