This work deals with numerical simulations of an annular burner with cross-section variations by using the FEM method. The main novelty is the introduction of the axial component of the mean flow in 3D simulations, which is usually neglected in the literature. The geometry investigated consists of an annular plenum chamber and an annular combustion chamber connected by 12 swirl burners. New insights are provided for a wide range of mean flow values, thus of Mach numbers. Firstly, a numerical assessment has been performed. Indeed, a simple annular geometry, which accurately approximates a real LP combustor, has been simulated and the results compared with the ones obtained with the software OSCILOS. The results achieved agree with the ones presented by Dowling and Stow [1], which demonstrated by applying a loworder one-dimensional model that the higher the mean flow velocity, the lower the frequencies and the growth rates gained.