Premixed flames stabilized behind the trailing edge of a semi-infinite cylindrical rod placed coaxially in a circular channel were investigated numerically within the diffusive-thermal model. Apart from the inverted flames, or V-flames, widely reported in the literature, the other kind of flames was observed for the Lewis number lower than unity. The main characteristic of such flames is confinement in the interior of a recirculating vortex formed behind the trailing edge. For a fixed Reynolds number, the flames of this kind exist within a finite range of the Damköhler number. Once the Damköhler number is fixed, they are observed for the Reynolds numbers above a critical value with no limit on large Re, assuming that flow remains laminar. Global linear stability analysis of the axisymmetric steady-state solutions of both kinds was performed. The ranges of the parameters where the axisymmetry-breaking bifurcation arises and the oscillatory behavior takes place were found. The results of the stability analysis were successfully compared with the direct two- and three-dimensional numerical simulations.