The effects of fluid rheology on the pressure drop in flow transverse to periodic arrays of circular cylinders (porosity=0.7) have been evaluated experimentally with several polyisobutylene solutions, at low Reynolds numbers. Care was taken to avoid degradation of the polymer during the permeation experiments. Specifically, the connection between extensional viscosity behavior and the flow resistance through the arrays has been evaluated experimentally with three dilute solutions of different molecular weight polyisobutylenes in polybutene at the same concentration. Fiber spinning of these solutions indicates that the apparent Trouton ratio of polymer contributions, at higher Deborah numbers, is proportional to the molecular weight. At Deborah numbers between 2 and 5, the (fRe) product attains a different asymptotic limit in each case. The high Deborah number limit of (fRe) is proportional to molecular weight, similar to the apparent Trouton ratios obtained from fiber spinning. In contrast, thefRe data for a strongly shear thinning solution of polyisobutylene in decalin do not show an upper limit even at a Deborah number of 8, based on a strain rate dependent relaxation time. Fluctuations in the downstream pressure are observed for the Boger liquids above the onset Deborah number, indicating the presence of an elastic instability. Hence, the assumption of a steady flow field appears to be untenable for computing the viscoelastic flow resistance in such media.