This work deals with the numerical simulation, by means of a finite element method, of the time-harmonic propagation of acoustic waves in a moving fluid, using the Galbrun equation instead of the classical linearized Euler equations. This work extends a previous study in the case of a uniform flow to the case of a shear flow. The additional difficulty comes from the interaction between the propagation of acoustic waves and the convection of vortices by the fluid. We have developed a numerical method based on the regularization of the equation which takes these two phenomena into account. Since it leads to a partially full matrix, we use an iterative algorithm to solve the linear system. © 2006 Elsevier B.V. All rights reserved.