Molecular dynamic simulations have been used to develop a mathematical model to investigate the extension of the polymer chains and the polymer chain orientations in the circular duct flows. The effects of pressure loss and molecular weight are also investigated on the polymer chain orientation. The model's outputs indicate that with increasing pressure loss and subsequently the shear stress at wall, the trace of the conformation tensor increases. This is interpreted as an increase in the extension of polymer chains and the polymer chain orientation in the flow direction. The model also predicts that the increase of the molecular weight of polymer results in decrease of the trace of the conformation tensor and the extension of the polymer chains. POLYM. ENG. SCI., 55:1196-1202, 2015. (c) 2014 Society of Plastics Engineers