This paper describes modifications of a Weissenberg Rheogoniometer (Model R‐16) which were made in order to diminish machine motions during stress transient measurements. Piezoelectric crystal load cells were installed in the torque and axial force measuring systems, and a cross‐beam support was added to increase axial rigidity. Start‐up and relaxation tests were performed with the modified instrument, the original torsion bar system, and the Rheometrics Mechanical Spectrometer, with polystyrene solutions ranging in zero shear viscosity from 700 to 56,000 poise. The shear stress transient data were practically independent of cone angle, platen diameter, and machine stiffness. After rigidification the normal stress transients showed relatively small variations with platen diameter and axial stiffness, but the effect of cone angle was still appreciable, as had been noted earlier by Meissner for melts. However, the normal stress transients appeared to approach an asymptotic behavior for the 4° and 8° gap angles. Flow visualization studies were made using a clear platen and dye-impregnated tracer solutions. The edge instability characterized by fluid expulsion from the gap did not appear to be associated with any nonuniform flow inside the gap. The edge instability occurred in a characteristic range of platen angular velocities for each solution.