The purpose of this study has been to develop an aerodynamic load model for the energy harvesting (traction) phase of leading-edge inflatable (LEI) kites operating in an airborne wind energy (AWE) context. The load model stems from multivariate polynomial regression analyses expressing the airfoil lift, drag and moment coefficients as polynomial functions of the angle-of-attack and 2D non-dimensional (relative to the chord length) shape parameters: non-dimensional tube diameter, maximum camber magnitude and chordwise position of maximum camber. The regression analyses relied on numerical data attained from computational fluid dynamics (CFD) simulations of the 2D flow fields around parameterised LEI wing profiles. The RANS equations, closed by the k-ω SST turbulence model, have been used for this purpose. The parameterisation and subsequent geometric construction of LEI wing profiles has been a key aspect of this study. As such, the effects of the shape parameters on the flow field have been assessed.