In this paper, non-intrusive polynomial chaos expansion (NIPCE) is used for forward uncertainty quantification and sensitivity analysis of thermoacoustic stability of two premixed flame configurations. The first configuration is a turbulent swirl combustor, modeled by the Helmholtz equation with an n - tau flame model. Uncertain input parameters are the gain and the time delay of the flame, as well as the magnitude and the phase of the outlet reflection coefficient. NIPCE is successfully validated against Monte Carlo simulation. It is observed that the first order expansion suffices to yield accurate results. The second configuration under investigation is a low order network model of a laminar slit burner, with the flame transfer function identified from weakly compressible CFD simulations of laminar reacting flow. Firstly the uncertainty and sensitivity of the growth rate due to three uncertain input parameters of the CFD model - i.e., flow velocity, burner plate temperature and equivalence ratio - are analyzed. A Monte Carlo simulation is no longer possible due to the computational cost of the CFD simulations. Secondly, two additional uncertain parameters are taken into account, i.e., the respective magnitudes of inlet and outlet reflection coefficients. This extension of the analysis does not entail a considerable increase in computational cost, since the additional parameters are included only in the low order network model. In both cases, the second order expansion is sufficient to model the uncertainties in growth rate. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.