Numerical simulations have been undertaken for the flow of test fluid M1 passing through the converging channel system designed to measure the extensional viscosity of polymeric liquids. The constitutive equation is an integral-type K-BKZ model with three relaxation times. The simulations have been performed for the full range of experimental measurements in this system, where the extensional deformation is dominant and the deformation rates are very high. Stable solutions have been obtained for the whole range even though the apparent shear rates reach 1300 s-1. Results concerning wall pressure difference between two pressure taps are compared with the experimental data measured from the pressure signals. The simulations are in good agreement with the experiments for the low range of flow rates at 21-degrees-C and for all flow rates at 30 and 40-degrees-C. The discrepancies at high flow rates for the lower temperature are apparently due to the appearance of a stationary bubble in the experiments that may have altered the pressure measurements. The pressure and stress distributions from the simulations show the flow characteristics of the converging channel system, which are difficult to verify by using experimental methods. The specially designed converging channel geometry makes the fluid M1 deform at a constant rate of extensional deformation near the centreline within the constant strain-rate section but only at low flow rates, and its normal stresses increase exponentially and then slowly relax in the subsequent cylindrical section. The extensional viscosity of fluid M1 obtained by simulations has been compared with the value from the experimental results. A more appropriate method of measuring extensional viscosity is recommended from the stress analysis in the converging channel flow field.