A new technique to measure elongational stress of low viscous viscoelastic fluids in transient planar elongational flow is developed. The measurement instrument for this technique consists of two parts, the squeeze flow cell and the birefringence measurement device. The squeeze flow cell consists a set of parallel plates and generates step planar elongational flow on the stagnation line on the center plain of the plates. The birefringence and the orientation angle along the stagnation line in the start-up flow and the relaxation after cessation of the flow are measured. The elongational stress can be calculated from these optical data when the stress-optical rule is applicable. The comparison between the velocity distribution and the birefringence measurement using the flow cell that has several dimensions shows that the elongation rate distribution is not constant along the stagnation line by the sidewall effect. However, it is confirmed that reasonable results can be measured under the flowing condition, W=40 mm, L=20∼40 mm, H₀=36 mm, where W and L denote the width and the length of the parallel plates and H₀ is the initial gap of parallel plates. The surfactant aqueous solution CTAB/NaSal, which is Maxwell fluid at low shear rate, is used as the sample of trial test of this technique. The planar elongational viscosity η_ep of this sample is measured by our technique and it is compared with shear viscosity η. Trouton ratio Tr (=η_ep/η) becomes almost 4 and this result demonstrates ability and practicality of our technique.