In this study, three EVAs (ethylene-vinyl acetate co-polymers) with different vinyl contents (VA) ranging from 9 wt% to 28 wt% (EVA9, EVA18 and EVA28) were melt blended with organo-clay to obtain polymer layered silicate nanocomposites. Filler intercalation and exfoliation were evidenced by X-ray diffraction. The melt state viscoelastic properties of EVA nanocomposites were studied to examine the influence of clay in altering the flow properties of these polymeric nanocomposites. The EVA18 and EVA28 nanocomposites exhibited remarkable difference in dynamic and steady shear properties compared to neat polymers. On the other hand, EVA9-5% nanocomposite did not exfoliate and exhibited rheological behaviour very similar to that of the neat polymer. Furthermore, the first normal stress difference was found to be dependent on the silicate loadings when measured at low shear stresses. The uniaxial extensional viscosity measurement indicated that the strain hardening was weaker in EVA nanocomposites compared to neat polymers. Environmental scanning electron (ESE)-microscopy elucidated a possible reason for reduced strain hardening in these systems.