The classical linear and original nonlinear (proposed by the authors) phenomenological and mathematical models for description of rheological behavior of viscoelastic heritable media (polymers above temperature of glassy-state, polymer composites etc.) have been analyzed. Nonlinear model of viscoelastic medium based on nonlinear Hammerstein operator has been proposed. We debated the regularization methods for inverse ill-posed by Hadamard problems and available for identifications of viscoelastic media models according to experimental data. To identification of linear model, which based on integral Fredholm’s operator of first kind we proposed to implicate Tikhonov’s method. To identification of nonlinear model with known in advance nonlinear function a method of statistic regularization by criterion of Baise has been developed. In case of model with nonlinear unknown function of nonlinearity we proposed a method of bit-linear approximation on the base of sequence Fredholm’s operator of first kind. An adequacy of theoretical approaches under consideration has verified by means of juxtaposition with real experimental rheological author’s data, which have been made for homo- and heterogeneous polymer media and composites using the set of up-to-date rheospectrometers.