The objective of this study was to apply a recently developed uncertainty quantification framework to the multidisciplinary analysis of a reusable launch vehicle (RLV). This particular framework is capable of efficiently propagating mixed (inherent and epistemic) uncertainties through complex simulation codes. The goal of the analysis was to quantify uncertainty in various output parameters obtained from the RLV analysis, including the maximum dynamic pressure, cross-range, range, and vehicle takeoff gross weight. Three main uncertainty sources were treated in the simulations: (1) reentry angle of attack (inherent uncertainty), (2) altitude of the initial reentry point (inherent uncertainty), and (3) the Young's Modulus (epistemic uncertainty). The Second-Order Probability Theory utilizing a stochastic response surface obtained with Point-Collocation Non-Intrusive Polynomial Chaos was used for the propagation of the mixed uncertainties. This particular methodology was applied to the RLV analysis, and the uncertainty in the output parameters of interested was obtained in terms of intervals at various probability levels. The preliminary results have shown that there is a large amount of uncertainty associated with the vehicle takeoff gross weight. Furthermore, the study has demonstrated the feasibility of the developed uncertainty quantification framework for efficient propagation of mixed uncertainties in the analysis of complex aerospace systems.