The propagation of the two-dimensional diffusive flame over combustible material is studied by solving appropriate steady-state conservation equations written in the coordinate system fixed on the flame front where the flame spread rate appears as an eigenvalue. It is shown that a solid fuel's mass balance is kept for any assigned value of the flame spread rate and therefore, the eigenvalue problem has not unique solution. A new algorithm for the flame spread rate prediction is proposed using the non-equilibrium thermodynamic approach. The steady flame spread is identified with the stationary thermodynamic state which is characterized, according to the theorem of Prigogine, by the minimal entropy production. The influence of free-stream velocity and ambient oxygen mass fraction on the flame spread process over thin sheets of paper is investigated.