Polymer melt elongation is one of the most important procedures in polymer processing. To understand its molecular mechanisms, we constructed an elongational flow opto-rheometer (EFOR) in which a high precision birefringence apparatus of reflection-double path type was installed into a Meissner＇s new elongational rheometer of a gas cushion type (commercialized as RME from Rheometric Scientific) just by mounting a small reflecting mirror at the center of the RME＇s sample supporting table. The EFOR enabled us to achieve simultaneous measurements of tensile stress sigma(t) and birefringence Delta n(t) as a function of time t under a given constant strain rate (epsilon) over dot(0) within the range of 0.001 to 1.0 s(-1). sigma(t) can be monitored upto the maximum Hencky strain epsilon(t) Of 7 as attained, in principle, with RME, while the measurable range of the phase difference in the birefringence was 0 to 250 pi: (0 to 79100 nm for He-Ne laser light) within the accuracy of +/-0.1 pi (+/-31.6 nm) up to E(r) N 4. The performance was tested on an anionically polymerized polystyrene (PS) and a low density polyethylene (LDPE). For both polymers sigma(t) first followed the Linear viscoelasticity rule in that the elongational viscosity, eta(E)(t) = sigma(t)/(epsilon) over dot(0), is three times the steady shear viscosity, 3 eta(0)(t), at low shear rate (gamma) over dot, but the eta(E)(t) tended to deviate upward after a certain Hencky strain epsilon(t) = (epsilon) over dot(0)t was attained. The birefringence Delta n(t) was a function of both Hencky strain epsilon(t) = (epsilon) over dot(0)t and strain rate (epsilon) over dot(0) in such a way that the stress-optical law holds with the stress-optical coefficient C(t) = Delta n(t)/sigma(t) being equal to the ones reported from shear flow experiments. Interestingly, however, for PS elongated at low strain rates the C(t) vs sigma(t) relation exhibited a strong nonlinearity as soon as sigma(t) reached steady state. This implies that the tensile stress reaches the steady state but the birefringence continues to increase in the low strain-rate elongation. For the PS melt elongated at high strain rates, on the other hand, C(t) was nearly a constant in the entire range observed. For LDPE with long-chain branchings, sigma(t) exhibited tendency of strain-induced hardening after certain critical strain, but C(t) was nearly a constant in the entire range of sigma(t) observed.