A study was made of the cone‐plate and parallel plate rheometry of two polymer solutions in order to obtain the viscometric functions τ, N 1 , and −N 2 by different methods. It is shown that it is possible to determine −N 2 by using normal stress data from the cone‐plate and parallel plate flows. A comparison of this −N 2 data with a more accurate method has shown good agreement. There is good agreement also between τ data from the cone‐plate and parallel plate flows. An analysis of some of the sources of error in cone‐plate and parallel plate rheometry has shown that for the current experiments on the Instron 3250 rotary rheometer, inertial effects, and changes in the cone‐plate or parallel plate gap during testing are insignificant. It is shown that the vertical force in the parallel plate rheometer depends on the parallel plate gap h, the force showing a plateau above a critical gap h c . From this work it was found h c /R∼0.05. The shear stress is unaffected by the gap. At this stage there is no known mechanism for this effect. For a 1.1% polyisobutylene solution it was found −N 2 /N 1 =0.11±0.03 and for a 7.14% polystyrene solution −N 2 /N 1 =0.31±0.05. These values agree with literature values for polystyrene and polyisobutylene solutions. For a given polymer, −N 2 /N 1 is only weakly dependent on the polymer concentration.