A detailed study of photoacoustics in circular resonators and waveguides in the presence of a gas flow is presented based on the Green's function method. In the first part of the paper, a wave equation is derived describing sound propagation in a flowing (perfect) gas due to a localized heating source. Analytical results are obtained for the acoustic pressure in the case of a constant gas flow subject to different boundary conditions. In the second part of the paper, the derived wave equation is solved for a parabolic flow profile using the finite-element method and results are compared with the constant-flow case. It is demonstrated that the gas-flow profile does not change the pattern of acoustic resonance frequencies significantly. In particular it is noted that the presence of flow gives rise to new peaks and we show that non-linearities with respect to the mean flow velocity appear already at 1% of the speed of sound at certain frequencies.