Abstract: Rotationally symmetric annular combustors are of practi- cal importance because they generically resemble combustion chambers in gas turbines and aeroengines, in which thermoacoustically driven oscillations are a major concern. We focus on thermoacoustic oscillations of azimuthal type, neglect the effect ofthe transverse acoustic velocity in the azimuthal direction, and model the heat release rate as being dependent only on the pressure in the combustion chamber. We study the dynamics of the annular combustor with a finite number ofcompact flames equispaced along the annulus, and characterise the flames’ response with a describing function. We discuss with broad generality the existence, amplitudes and the stability of standing and spinning waves, as a function of: 1) the number of the burners; 2) the damping in the chamber; 3) the flame describing function. These have implications on industrial applications, the future direction of investigations, and for what to look for in experimental data. We then present as an example of application the first theoretical study of triggering in annular combustors, and show that rotationally symmetric annular chambers can experience stable standing solutions.