A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows: a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.