In this paper we present a new approach for calculating viscoelastic ows. The polymer stress is not determined from a closed-form constitutive equation, but from a microscopic model. In this description, we replace the collection of individual polymer molecules by an ensemble of con guration elds, repre- senting the internal degrees of freedom of the polymers. Similar to the motion of real molecules, these con guration elds are convected and deformed by the ow and are subjected to Brownian motion. We incorporated this eld description in a nite element calculation. An important advantage of our approach is that the di culties associated with particle tracking of individ- ual molecules are circumvented. In order to validate our approach and to demonstrate its robustness, we present the results for the start-up of planar ow of an Oldroyd-B uid past a ! cylinder between two parallel plates. The results are very promising. We nd excellent agreement between the results of the con guration eld formulation and those obtained using a closed-form constitutive equation. Moreover, the microscopic method appears to be more robust than the conventional macroscopic technique.