Elongational deformation was conducted on a polystyrene-block-polyisoprene-block-polystyrene (SIS) triblock copolymer (Kraton D1107) having soft spherical microdomains composed of polyisoprene block chains in a hard matrix composed of polystyrene block chains. The extensional flow behavior of triblock copolymer melt that exhibits a cubic phase has been examined using elongational viscosity with $varepsilon$$_{0}$ between 0.03 and 1.0s$^{-1}$ at different temperatures. In this study, the transient uniaxial viscosity of the triblock copolymer melts first gradually increased with increasing time, following the linear viscoelastic rule in which the uniaxial extensional viscosity is three times the shear viscosity. After a certain strain, the extensional viscosity showed rapid increase, which was referred to as strain hardening. The TEM and SAXS data of samples showed that the spherical PS-domain is deformed and oriented along the direction of elongation. When the SAXS patterns and TEM were examined, it was found that the spheres were transformed into cylinder microstructures with short-range order.