Numerical simulations have been undertaken for the flow of three polyethylene melts, two low-density (LDPE) and a linear low-density (LLDPE), around a cylinder placed between parallel plates. Polyethylene melts have been the subject of previous extensive rheological characterizations. The flow geometry corresponds to a 2:1 and a 1.6:1 gap/diameter ratio used in experimental studies for flow-induced birefringence (FIB) measurements. The constitutive equation of this work is an integral-type K-BKZ model with a relaxation spectrum, which fits well experimental data for the shear viscosities and the normal stresses as measured in shear flow. The model has been properly modified to account for strain-thickening in planar extensional flows, such as those studied here. Stable numerical solutions have been obtained for a wide range of flow rates and used to compare the K-BKZ model predictions with the experimental observations for FIB. Good agreement is obtained for the birefringence predictions in all cases, provided that the right amount of strain-thickening has been assumed for the planar extensional viscosity. The simulations are also in agreement with previous simulations for the same problem using multi-mode differential constitutive models. The drag force exerted by the fluid on the cylinder has been calculated and reported to be a decreasing function of the flow rate.