Stochastic models are considered as a numerical tool for simulating the dynamic behavior of polymeric fluids. At small Deborah number, straightforward numerical integration of these models is both costly because of the separation of time scales and inaccurate because of the large numerical fluctuation. A new technique, motivated by the recently developed heterogeneous multi-scale method (HMM), is introduced to overcome these problems. (C) 2004 Elsevier B.V. All rights reserved.