Numerical computations are employed to study the flow field produced by a four‐roll mill. The radius of the cylindersa, the cylinder spacing 2b, and the size 2lof the square container are varied to assess the effects on the kinematics of the flow field. It is found that a ratio ofa/b=0.625 withl/b≥3.0 produces the best approximation to a pure extensional flow. With these parameter values, the extension rate remains constant with an error of less than 1% over an axial regionx/b≤0.5. By contrast, the commonly accepted designa/b=0.772 suggested by Fuller and Leal [J. Polym. Sci. Polym. Phys.19, 557 (1981)] produces a variation in extension rate of 50% over the same region. Streamline patterns and velocity gradient error contours are presented for these two designs.