A combined finite element and Brownian dynamics technique (CONNFFESSIT) is used to predict the steady-state flow field around an infinite array of square-arranged cylinders using kinetic theory models. A finitely extensible elastic (FENE) dumbbell model and a modified reptation model are considered. Since Brownian dynamics simulations are used to predict the stresses in the flow field, no closure approximations are necessary in the models, such as the Peterlin approximation, or independent alignment. Comparisons are made with analogous models that have closed-form constitutive equations, namely the FENE-P dumbbell, and Doi and Edwards reptation model with independent alignment using the same numerical technique. The modified reptation model contains information about the entire chain configuration instead of just single segment orientations. In this way, the problems involved with reversing flows for reptation with independent alignment can be avoided. Since the flow field presents alternately converging and diverging flows for fluid particles, it offers an important test for reptation models in reversing flows. We find significant quantitative difference between the predictions of the approximate and the more realistic models. For example, the FENE-P dumbbell underpredicts the magnitude of the normal stresses by as much as 25%, reptation with independent alignment underpredicts the magnitude of the normal stresses by as much as 22%. The calculations presented here are a starting point towards the realistic prediction of the onset of instability seen experimentally in these flows.