The influence of an elongational flow on the morphology of PE/clay nanocomposite drawn fibers was studied. An increase of the elastic modulus and the tensile strength as well as a decrease of the elongation at break are observed with increasing draw ratio. The applied elongational gradient orients the polymer chains and the clay particles along the spinning direction. When the applied flow results in the formation and the orientation of exfoliated nanoparticles, a pronounced increase of the mechanical properties is observed. The dispersed clay particles can be broken and oriented by the extensional flow, which might indicate a flow‐induced intercalated/exfoliated morphology transition.