Uncertainty quantification (UQ) is the process of quantitative characterization and propagation of input uncertainties to the response measure of interest in experimental and computational models. The input uncertainties in computational models can be either aleatory, i.e., irreducible inherent variations, or epistemic, i.e., reducible variability which arises from lack of knowledge. Previously, it has been shown that Dempster Shafer theory of evidence (DSTE) can be applied to model epistemic uncertainty in case of uncertainty information coming from multiple sources. The objective of this paper is to model and propagate mixed uncertainty (aleatory and epistemic) using DSTE. In specific, the aleatory variables are modeled as Dempster Shafer structures by discretizing them into sets of intervals according to their respective probability distributions. In order to avoid excessive computational cost associated with large scale applications, a stochastic response surface based on point-collocation non-intrusive polynomial chaos has been implemented as the surrogate model for the response. A convergence study for accurate representation of aleatory uncertainty in terms of minimum number of subintervals required is presented. The mixed UQ approach is demonstrated on a numerical example and high fidelity computational fluid dynamics study of transonic flow over RAE 2822 airfoil.