Abstract In this study, the synthesis of inorganic materials by combustion of solid cylindrical preforms is addressed. The reaction between two solid reactants is analyzed when the reaction proceeds in the combustion regime. This process is characterized by a thin propagating reaction front. The elevated temperature levels reached at the combustion front usually prevent this process from being carried out under ideal adiabatic conditions. The planar model of propagation manifests then as a curved moving front. Previous studies on this subject have followed the approach of lumping the temperature in the radial direction to make the problem more tractable. In this work, such an approach is discarded and a two-dimensional stability analysis is performed. It is shown that planar propagation can become unstable, developing into (i) auto-oscillations, (ii) spinning combustion with a single or multiple heads located near the outer surface, and (iii) multiple-head spinning waves with one or multiple heads near th...