The traditional approach to space mission design considers deterministic dynamics, relying on a Guidance, Navigation and Control (GNC) system to manage uncertainty dispersions. To simplify the iterative process of trajectory design, reduce the burden on GNC, and increase mission safety, this thesis investigates the use of uncertainty propagation to robustify a deterministically-optimal atmospheric entry trajectory. A hybrid Gaussian Mixture Model-Polynomial Chaos Expansions method is optimised and used to generate analytical expressions of the entry corridor statistics as a function of 16 uncertainty sources and five decision variables. These expressions reduce the design space and directly handle stochastic constraints, simplifying the subsequent optimisation. The method is validated on the HORUS-2B vehicle and reference trajectory, widening the entry corridor margins to 2-sigma bounds with errors in the order of 2%. The output of this thesis is a generic stochastic optimisation methodology that is more efficient than traditional optimisation with Monte Carlo simulations.