Non-linear models of viscoelastic media behavior based on Maxwell, Jeffrice and Foight-Kelvin elements are discussed. Above elements are linear but a function of linearity is entered as variation of value of stresses. These models have some theoretical interest, but from practical aspect are useless, because of algorithms of identification and functions of non-linearity of those are unknown. Perspective by the authors opinion are the some integral models, in particular a variant, which let us the non-linearity of material function factorizes as non-linear “damping-function” and an independent linear material function. A novel method for identification of above model for finite deformations has been developed. The method is based on construction of relaxation spectra of a viscoelastic medium by finite deformation value using the method of bit-linear approximation of non-linear function developed by the author previously. Evaluation of “damping-function” is made by experimental data by using of non-linear regression by minimum mean-square mistake and further the algorithm of regularization of a problem. Adequacy of the method of identification has been taken in real experiments for elastomer composites on base of natural rubber matrix filled with technical carbon.