A one dimensional numerical model is proposed to study the counter-current fire spread in a pine needles fuel bed confined in a tube. The physical mechanisms which control the fire spread and the interactions between the gas flow and the solid fuel particles are described using a multiphase formulation. The set of partial differential equations which governs the physical behavior of the gas flow and of the solid fuel bed is solved using a finite volume method. To describe accurately the small area where the thermal degradation (drying, pyrolysis, char combustion) of the solid fuel occurs, the calculations are carried out using an adaptative grid algorithm consisting in refining locally the grid on both sides of the pyrolysis front. The computation results have not been confronted with experimental measurements, therefore the objective of this study is to highlight the behavior of this physical system according to the rate of air supply. While varying the inlet flow velocities ranging from 2 to 30 cm/s, the numerical results show the existence of two modes of propagation, respectively limited by the arrival of oxygen and the production of combustible gas.