This paper reports the properties of highly oriented nanocomposite tapes based on isotactic PP and needle‐like sepiolite nanoclay, obtained by a solid state drawing process. The intrinsic 1D character of sepiolite allows its exploitation in 1D objects, such as oriented polymer fibres and tapes, where it can be uniaxially oriented upon drawing. A synergistic increase in mechanical properties is presented for highly drawn tapes (λ ≤ 20) and low filler loadings (≤2.5 wt.‐%), which can not be simply explained by micromechanical composite models. Instead, mechanical properties are intimately related to the dispersion state of the nanoclays in PP, the rheological properties of the nanocomposites and the polymer morphology.