The problem of modelling sound waves in a two-dimensional wave-guide of general shape carrying a mean flow is addressed. The mean flow may be inhomogeneous but is irrotational. A convective wave equation for the velocity potential is derived. It is in a form suitable for generalizing an earlier developed theory for a stable modelling of acoustic waves in quiescent waveguides with complicated geometry to also include a mean flow. The theory is illustrated with numerical results for reflection and transmission demonstrating the effectiveness of the method for low and medium frequencies.