For the critical evaluation of the rheological equations of state for polymer solutions, steady-state and dynamic experiments including transient normal and shear stress measurements are required. It has been found that the normal force measurement system in the Weissenberg Rheogoniometer (WRG) is not suitable for the transient normal stress measurement. Therefore, the leaf spring in the WRG was replaced by one of a set of cantilevers with various rigidities, and the servo system was discarded. The present investigation reveals that the transient normal stress data depend on the rigidity of the cantilevers used. Thus, a series of normal stress measurements with several cantilevers was made to obtain reliable data. The results show that the normal forces in the transient experiments approach asymptotic values as the cantilever rigidity increases. Therefore, these asymptotic values were taken as representative of the material response. The present study indicates that a forced damped vibration mechanism may be responsible for the systematic dependence of the transient normal forces on the cantilever rigidity. Furthermore, the shear stress response of glycerin under a suddenly started shear flow suggests that the undershoot commonly observed in the stress growth experiment may be an apparatus response rather than a material property.