The aim of this study is to predict the elastic response of poly(lactic acid) (PLA) electrospun nanofibre scaffolds through mathematical models based on homogenisation and the differential replacement method (DRM). These models principally seek to determine and analyse the effects of the internal morphology of the nanofibres on the effective Young's modulus of polymer nanofibre scaffolds. The microstructure of the nanofibres was first characterised by SEM, XRD, DSC, AFM, and TEM techniques. From this characterisation, strong evidence of a hierarchical core-shell structure was found. With the experimental data, it was possible to design and validate better models than those currently used. In addition, the effects of the electrospinning parameters, such as take-up velocity and thermal treatment, were analysed and correlated with the morphology and the elastic properties of the nanofibres and their scaffolds. To validate the models' results, we conducted a series of uniaxial tensile tests on the PLA nanofibre scaffolds. Using the data from the nanofibre measurements, the homogenisation approximations and the model based on the DRM predicted an effective Young's modulus of 667 and 835 MPa, respectively. The predicted data were in excellent agreement with the experimental results (685-880 MPa). These models will be useful in understanding and evaluating the structure-property relationships of oriented nanofibre scaffolds for medical or biological applications.