The need for robust optimisation in aircraft conceptual design, for which the design parameters are assumed stochastic, is introduced. We highlight two approaches, first-order method of moments and Sigma-Point reduced quadrature, to estimate the mean and variance of the design’s outputs. The method of moments requires the design model’s differentiation and here, since the model is implemented in Matlab, is performed using the automatic differentiation (AD) tool MAD. Gradient-based constrained optimisation of the stochastic model is shown to be more efficient using AD-obtained gradients than finite-differencing. A post-optimality analysis, performed using AD-enabled third-order method of moments and Monte-Carlo analysis, confirms the attractiveness of the Sigma-Point technique for uncertainty propagation.