Flame stabilization and blowoff over a porous cylinder, from which the gaseous fuel is injected into the incoming air stream, is studied theoretically. The mechanism of stabilization for envelope and side flames is upstream heat and mass diffusion, whereas wake flame depends on the recirculating flow. The normalized model includes the two-dimensional continuity, Navier-Stokes’ momentum, energy and species equations with a one-step overall chemical reaction and second-order, finite-rate Arrhenius kinetics, and it is solved numerically. The effects of Damkohler number (Da) and dimensionless fuel ejection rate (-fw) are investigated separately. The envelope flame, a pure diffusion flame, exists when Da is greater than 13.64. As Da is decreased by increasing the incoming oxidizer velocity or stretch rate, the envelope flame is converted into a side- or a wake-flame, which the former shows both premixed- and diffusion-flame characteristics and the latter is a premixed flame. A flow recirculation behind the cylinder is found for every case of flame. When the fuel ejection rate is reduced to a certain value, envelope flame loses a lot of heat to surface and transforms into wake flame directly.