The objective of the proposed work (Phases I and II) is to develop uncertainty quantification methodologies and software suitable for use in CFD simulations of aerodynamic flows, ranging from sub-sonic to hypersonic. We will address both pressure and density-based methods, as well as the class of algorithms addressing all-Mach number flows. The software developed here will be based on an existing unstructured finite volume CFD solver, TETHYS, which has been developed by Jabiru Software and Services. A central focus of the proposal is the development and evaluation of generalized polynomial chaos (gPC) methodologies for uncertainty propagation. In Phase I, we will develop non-intrusive sparse-grid based adaptive collocation techniques for all-speed flows to address the curse of dimensionality and to resolve discontinuities and non-linearities in random space. We will evaluate the feasibility of implementing stochastic Galerkin techniques non-intrusively through operator overloading. Phase I will address airfoil flow across the range of Mach numbers. Phase II will address more general implementations of feasible approaches, application to more complex aerodynamics simulations, as well as implementation on parallel platforms.