The kinematics and the principal stress difference were determined for a 5% solution of polyisobutylene in mineral oil undergoing plane stagnation flow. These results were then used to evaluate four constitutive equations. The stagnation flow data were obtained for flow into a “T” shaped channel with measurements taken along the centerline. The kinematics consisted of the velocity distribution, and they confirmed the presence of a stagnant zone in which there was no downward flow. The velocity and position data, in a reduced form, were found to superimpose for several flow rates so that a master curve could be used with the constitutive equations to predict the stress differences. The latter were then compared with stress differences determined using a stress‐birefringence apparatus constructed for this purpose. The experimental stress difference along the centerline went through a maximum when plotted against position. The following constitutive equations were evaluated: the White‐Metzner, the Oldroyd 3‐constant, the BKZ, and the WJFLMB equations. The rheological parameters in these equations were obtained using stress‐birefringence data for steady shear flow through a rectangular channel. Each of the equations correctly predicted a delayed normal stress difference growth as a function of time. The WJFLMB model was found unsatisfactory in its ability to predict the magnitude of the stress difference. All the remaining models did a reasonably good job in their predictions with the Oldroyd model being slightly superior at high deformation rates.