In the work the new approach to modeling the industrial process of polystyrene production has been submitted. The approach has been worked out with allowing for describing the peculiarities of the process kinetics in a reactor with accounting of the real structure of substances fluxes. The effective method for the identification of the parameters of the mathematical model has been developed. The undiscounted random factors are considered as a summary unobserved noise which is described with the help of Gauss law and forms the random sequences of the uncontrolled perturbations with a zero average value and with unit variance. Thus, according to the stochastic approach a few unobserved variables, which characterize a certain influence of the random factors, are included to the apriority model. On such an approach the mentioned above random factors are described in the form of additive time-correlated random perturbations. Persistency of the industrial process allows assuming that values of all the time-dependent factors at the moment depend only on the preceding moment. The novel methods for identifying the mathematical model have been applied to describing the polystyrene production process with the best evaluations of the process parameters.