In this work, the effect of extensional flow on the morphology of polystyrene-b-poly(ethylene-co-butylene)-b-polystyrene (SEBS) triblock copolymers and their clay-containing nanocomposites was evaluated. Four types of SEBS copolymers with different block compositions and cylindrical morphology were chosen to understand the effects of cylinder orientation and state of clay dispersion on the evolution of morphology during extensional flow. The effect of clay concentration (ranging from 2.5 to 7.5 wt. %) was also studied. The samples were subjected to extensional flow using a Sentmanat extensional rheometer attached to a rotational rheometer at Hencky strain rates varying from 0.01 to 20 s(-1). Small angle X-ray scattering analysis was subsequently performed to evaluate the morphological changes caused by extensional flow. When preoriented block copolymers [SEBS-30% PS (polystyrene)] and their nanocomposites undergo elongation, the styrene cylinders and clay nanoparticles align themselves in the flow direction and their rheological behavior and morphological evolution are influenced by the stretching direction (longitudinal and transverse), strain rate magnitude, clay concentration, and dispersion state of the clay nanoparticles. When isotropic block copolymers (SEBS-13% PS) undergo elongation, it was observed that the PS cylinders only exhibit structural alignment in the stretching direction in the presence of clay. Block copolymer molecules can exhibit different relaxation times depending upon the volume fraction of PS domains (13% or 30%). The addition of clay, however, hinders complete relaxation, helping to promote a permanent domain alignment after flow cessation, especially in hard-to-align copolymers. (C) 2016 The Society of Rheology.