The steady state shear and linear viscoelasticproperties of both isotropic and liquid crystalline solutions of the rigid chain polymer poly‐p‐phenyleneterephthalamide in sulfuric acid have been determined. Both the primary normal stress coefficient and the linear viscoelasticproperties show the same characteristic concentration behavior as does the viscosity. The unique rheological properties of the anisotropic phase can be attributed to the formation of a suspension of highly ordered regions in a matrix of isotropic fluid. The rheological properties were compared against the Bird‐Carreau model and Hand's anisotropic fluid theory. Remarkably good agreement was found between the Bird‐Carreau model and data especially at high shear rates. This suggested that at high shear rates very little difference may exist between anisotropic and isotropic phases. Hand's model was more applicable to solutions which were only slightly anisotropic.