Numerical simulations have been undertaken for the flow of a 5 wt. % polyisobutylene (PIE) solution in tetradecane (C14) around a cylinder placed between parallel plates. The PIE solution has been the subject of an extensive theological characterization and the flow geometry corresponds to the one used in a previous study for laser Doppler anemometry and flow-induced birefringence measurements. The constitutive equation used is an integral-type K-BKZ model with a relaxation spectrum, which fits well experimental data for the shear and elongational viscosities and the normal stresses as measured in shear flow. Stable numerical solutions have been obtained and used to compare the K-BKZ model predictions with the experimental data reported recently by Baaijens. The velocity and shear stress values predicted by the simulation are in excellent agreement with the experimental ones. Very good agreement is also obtained for the predictions of the first normal stress difference both before and after the cylinder, in sharp contrast with previous experimental results, which had shown a much slower relaxation of the stresses. The drag force exerted by the fluid on the cylinder has been calculated and reported to be a decreasing function of the Deborah number De.