In the field of the scattering of acoustic waves from structures immersed in an infinite fluid medium, a coupling between the EQI boundary element code and the ATILA finite-element code is available. The boundary element method used is the Helmholtz integral equation. At some frequencies, called irregular frequencies, this integral formulation presents an infinite number of solutions. This problem is solved with the help of the Jones method: The integral equations system is overdetermined by null-field equations. Many structures are axisymmetric. So, it is attractive to develop a modeling that is able to keep the advantages of the axis of symmetry and to take into account an incident wave of any direction. This numerical tool is performed using a harmonic cylindrical decomposition. In this case, the mesh is restricted to the line of the structure included in the meridian plane. Compared with three-dimensional modeling, this new possibility provides the following advantages: either a reduction of the computation time, the memory size, and the disk storage space and an improvement of the numerical behavior; or an increase of the maximum frequency. Comparison between numerical results and experimental data is presented.