The objective of this study was to demonstrate the use of a combined sparse sampling and stochastic expansion approach for efficient and accurate uncertainty quantification of high-fidelity, hypersonic reentry flow simulations, which may contain large numbers of aleatory and epistemic uncertainties. Stochastic expansion coefficients were obtained using the point-collocation non-intrusive polynomial chaos technique under sparse sampling conditions, utilizing a number of samples less than the minimum number required for a total order expansion. This study introduced two methods of measuring the accuracy of the expansion coefficients as well as their convergence with iteratively increasing sample size. The sparse sampling solution technique and accuracy and convergence measures were demonstrated on two model problems. The first was a model for stagnation point, convective heat transfer in hypersonic flow. Mixed uncertainty quantification analysis results showed that accurate expansion coefficients could be obtained with half the number of samples required for an analytically obtained total order expansion. The second problem was a high-fidelity, computational fluid dynamics model for radiative heat flux on a Hypersonic Inflatable Aerodynamic Decelerator during Mars entry. The model consisted of 93 uncertain parameters, coming from both flow field and radiation modeling. Results indicated that an accurate surrogate model could be obtained with only about 15% of the number of samples required for a total order expansion when compared to previous work.