On the basis of air heater characteristics, a new computational model was developed in this paper, which was aimed at investigating acoustics and instabilities in air heaters. This model included the effects of mean flow, viscosity, entropy waves, non-linear acoustics and realistic boundary conditions. In addition, it was practical for air heaters with hundreds of injectors, complex configurations and geometries. Analytical solutions of acoustics in a closed rectangular cavity were used to verify and validate the computational model. It was shown that the predicted critical parameters of air heater agreed well with the experimental data or design values. This model predicted the self-excited spinning tangential modes without any preliminary assumptions about them. Traditional combustion response function assumes that combustion mainly takes place in a so-called rapid combustion zone, and this zone is usually modelled as a disc in the combustor near the injection head. However, in practice, the flame has a spatial distribution. This paper described the effect of flame spatial distribution on predictions of oscillation frequency and mode. It was found that frequency and mode shape of oscillations closely depended on the length of the heat release zone. Comparison of different heat release zones indicated that the increment of heat release length exhibited an increased tendency toward lower-order longitudinal modes, when the heat release zone was located near the faceplate where it was the pressure antinode of the longitudinal mode. Modulation of heat release length might cause bifurcations between standing and turning modes. A noticeable tendency was toward higher-order standing tangential mode with increasing heat release length. Finally, theoretical analysis of the modal behaviour, i.e. standing or spinning waves, was performed.