The paper deals with the assessment of the influence of morphological parameters of a 2Drandom short fibre composite on its effective elastic properties. A double-scale 2D finiteelement approach is used and periodic representative volume elements are generatedaccording to the model with an n-order approximate geometry. This one isa recent and powerful tool to generate meshes in the context of complex microstructuressuch as random fibre composites. Impact of three morphological features namely, aspectratio, tortuosity of fibres and width of the interphase area, is investigated. Numericalresults are provided for several contrasts of properties and volume fractions of fibres.