Experimental studies about the effect of block copolymerized structures on the uniaxial elongational viscosity were performed. Two poly (styrene-block-butadiene-block-styrene) (SBS, S/B weight ratio=4/6) samples with linear and star (4arms) structures were used for the elongational viscosity measurement at constant strain rates. The block copolymer samples exhibited the strain-softening elongational viscosity. This property was in contrast to the strain-hardening elongational viscosity which is observed for homopolymer melts. The cause of the strain-softening property was analyzed from the structural change by small angle X-ray (SAX) and transmission electron microscope (TEM). The lamellar structures were more oriented and became longer along the elongational direction e elongation, while the lamellar thickness remained almost constant. he obsrvation inicates that the laellar structures, instead of the SBS molecules, were oriented and stretched. The rheological discussion on the strain-softening elongational viscosity was also carried out by the BKZ model. The damping functions of the block copolymers from step-shear relaxation experiments showed larger decrease than that of the Doi-Edwards prediction. The structural change observation and the BKZ analysis suggested that the largely decreased damping functions are due to the lamellar orientation and cause the strain-softening elongational property.