Numerical simulations of the unsteady flame propagation inside a rotating vessel have been performed, providing a description of the flame behaviour from ignition to the unusual quenching of homogeneous and flammable methane-air mixtures, as experimentally observed. A detailed analysis of these results is presented that shows several interesting features of this flame. Particularly interesting are the detection of the flow structure at the edge of the flame near the side walls and of the action of a sliding component of the strain rate tensor. It has been also recognized that, just before the extinction, the flame becomes more intense and after this phase, it is difficult to separate well the unburnt and heavy fresh mixture from the hot and light burnt gases previously distinctly separated by the action of the centrifugal forces.