Two structural models of the thermo-elastic behavior of strace-reinforced media are offered at the general anisotrotry of the comtronent materials of the comtrosition. As criteria of equivalence of fibrous comtrosition to a fictitious homogeneous anisotrotric material the equality strecific free energy and the Gibbs thermodynamic energy in thtd are used. It allows determining the utrtrer and lower boundaries of the effective stiffness of reinforced materials. Comtrarison with extreriments was trerformed. It was shown that lower bounds for effective rigidities better agreed with the extrerimental data than the calculated values of the same values that are defined on the basis of other structural models.