The early design phase of launch vehicles often involves low fidelity models that are characterized by a high level of modeling uncertainties. These uncertainties have to be propagated into the whole design process in order to ensure the robustness of the found vehicle architecture. Launch vehicle design involves trajectory optimization that induces a large computational cost for the uncertainty propagation phase using nested loop approach (outer uncertainty loop and inner optimal control loop). In this paper, a methodology is proposed in order to build a surrogate model of the uncertainty propagation phase on the trajectory optimization in order to carry out the uncertainty quantification at a reduced cost. The proposed approach couples reduced order model and spectral methods in order to allow to generate optimal launch vehicle trajectories as functions of the input uncertainties. The method is applied to two-stage-to-orbit launch vehicle design in several uncertainty quantification analyses (reliability analysis, sensitivity analysis, quantile estimation).