An apparatus was developed for measurements of the flow birefringence of polymer solutions in time‐dependent flow, such as the start and the sudden cessation of steady shear flow. A linearly polarized light beam was led through the sample held in the gap between two coaxial cylinders in relative rotation, and then through an analyzer. The intensity of the transmitted light was measured as a function of time. The birefringenceΔnand the extinction angle χ were evaluated from light intensities for which the angles between the direction of flow and the direction of polarization of the incident beam were −22.5°, 0°, 22.5°, and 45°, respectively. Measurements were performed at 35°C on an 8% solution of polystyrene of weight average molecular weight3.0×106in chlorinated biphenyl. The stress‐optical law was applicable to the solution at the start and on the cessation of steady shear flow over the range of rate of shear, from6.6×10−3 sec−1to2.14×10−1 sec−1,studied. The stress‐optical coefficient obtained was5.9×10−9 Pa−1,in good agreement with literature values. The first normal stress difference was evaluated from the birefringence data with the use of the stress‐optical law. The normal stress in relatively short times after the start of shear flow was consistent with that predicted from the second‐order fluid theory.