The classical model of linear and nonlinear viscoelastic fluids. It was established experimentally that the main type of nonlinearity arises when large deformations and is associated with a change in the shape and position of the axis of the relaxation spectrum of relaxation times. On the basis of the integral operator synthesized Hammerstein type nonlinear viscoelastic model environments. To identify the model proposed and rigorously justified regularization method based on functional and Tikhonov regularization method based on the criterion Bayes. A piecewise linear approximation of a nonlinear integral operator Hammerstein type. Spend a sequence of natural-computing experiments viscoelastic characteristics of heterogeneous polymer media for large deformations using a piecewise linear approximation of a nonlinear model of Hammerstein type.