In this work we present Reynolds-averaged Navier-Stokes (RANS) simulations of the flow past the constant design shape of a leading-edge inflatable (LEI) wing. The simulations are performed with a steady-state solver using a k-ω SST turbulence model, covering a range of Reynolds numbers between 10⁵ ≤ and ≤ 15 × 10⁶ and angles of attack varying between-5° and 24°, which are representative for operating conditions in airborne wind energy applications. The resulting force distributions are used to characterize the aerodynamic performance of the wing. We found that a γ-Re_θ transition model is required to accurately predict the occurrence of stall up to at least Re= 3 × 10⁶. The work highlights similarities with the flow past a two-dimensional LEI airfoil, in particular, with respect to flow transition and its influence on the aerodynamic properties. The computed values of the lift and drag coefficients agree well with in-flight measurements acquired during the traction phase of the LEI wing operation. The simulations show that the three-dimensional flow field exhibits a significant cross flow along the span of the wing.