A new method for numerical calculation of polymeric flow based on simulation of molecular models of polymers is presented. The approach directly combines streamline finite element method with stochastic simulation of molecular models and thus obviates the need for a constitutive equation to describe the fluid. The problem considered for testing the method is the two - dimensconal steady flow of an Oldroyd - B fluid past a circular cylinder between two parallel plates. A comparison is made between the numerical results obtained using the new approach and those obtained using the closed- form constitutive equation of the Oldroyd -B model.