A stochastic rheological model for the calculation of polymer stress in polymeric fluids is developed and evaluated. The model is microscopic-based and combines aspects of reptation, modified network and continuum models. A concentrated Polyisobutylene (PIB) solution is simulated for material functions in various rheometric flows. Comparisons made with available experimental data shows that the model predicts well the qualitative material behavior of the fluid in the rheometric flows considered. In most cases, the predictions agree quantitatively with the available experimental data.