In this study, the mechanical strength and the AC short term breakdown strength of polystyrene‐b‐poly(ethylene‐co‐butylene)‐b‐polystyrene (SEBS) thermoplastic elastomer clay‐containing nanocomposites have been investigated as function of their morphologies. The SEBS/clay nanocomposites with tailored morphologies were prepared previously by different processing techniques. They featured different orientations of clay platelets as well as polystyrene (PS) block nanodomains, namely: isotropic, oriented, and partially oriented morphologies. In unfilled SEBS matrices, the mechanical strength was mainly tuned by the orientation of PS block nanodomains. A good correlation between the dielectric breakdown strength and the mechanical stiffness was observed overall: the higher the mechanical strength was, the higher the breakdown strength was. In the nanocomposites, the orientation of clay platelets as well as the degree of order and the characteristic sizes of the block copolymer domains were seen to affect strongly the breakdown strength behavior in addition to the mechanical strength. In particular, the partially oriented morphology achieved by film blowing extrusion exhibited the maximum increase of the breakdown strength by 25% with optimized mechanical stiffness evaluated between that of the oriented morphology as a lower limit and that of the isotropic morphology as an upper limit. POLYM. ENG. SCI., 58:E174–E181, 2018. © 2018 Society of Plastics Engineers