The flow of a low‐density polyethylene (LDPE) melt in a 10:1 slit‐die contraction at 150°C is simulated by using a two‐dimensional finite element program, and comparisons are made with the experiments of Kramer (1993) who used laser Doppler velocimetry to measure the velocity field at several flow rates. The LDPE melt is modeled by a Rivlin‐Sawyers integral constitutive equation with a spectrum of relaxation times where the parameters were determined from shear and elongational data. Evaluation of the general performance of our model and simulation at several flow rates shows that the simulation accurately predicts the vortex size but underpredicts the velocity overshoot along the centerline. Repeating Kramer’s particle tracking analysis of the flow field at one flow rate for a given set of streamlines we find good quantitative agreement for the elongation rates and relative stretch ratio, but we find our simulation generally underpredicts the shear rates and relative shear strain.