Computational fluid dynamics simulations of hypersonic, planetary entry flows and radiative heating predictions possess a significant amount of uncertainty due to the complexity of the flow physics and the difficulty in obtaining accurate experimental results of molecular level phenomena. In addition, the complexity of the flow physics requires high-fidelity, numerical models, which are computationally expensive. Therefore, quantifying the uncertainty in such models with classical sampling approaches becomes infeasible due to the large number of model evaluations required to obtain the statistics with desired accuracy. In this chapter, a computationally efficient means of uncertainty quantification was introduced and demonstrated for the prediction of radiative heating during Mars entry. The approach was to construct a surrogate model using a sparse approximation of the point-collocation non-intrusive polynomial chaos method. While polynomial chaos methods suffer from the curse of dimensionality, the sparse approximation method alleviates the cost for large-scale problems, such as the high-fidelity numerical modelling of planetary entry flows with radiative heating. The results show that an accurate stochastic surrogate model could be constructed with only 500 samples of the computational model. This is about 10% of the cost to construct the same surrogate model without the sparse approximation and corresponds to a significantly less number of samples than required for a pure sampling-based uncertainty quantification approach.