Numerical methods are mostly used to predict the acoustic pressure inside duct systems. In this paper, the development of a numerical method based on the convected Helmholtz equation to compute the acoustic pressure inside an axisymmetric duct is presented. A validation of the proposed method was done by a comparison with the analytical formulation for simple cases of hard wall and lined ducts. The effect of the flow on the acoustic pressure inside these ducts was then evaluated by computing this field with different Mach numbers.