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