Unsteady burning of a fuel bed is often encountered in urban and wild land fires. Two kinds of fuel bed are examined. They are a liquid pool and a porous bed. The fuel bed is ignited at one end by a heat source. The fluid flow, heat and mass transfer, combustion and gasification of the fuel bed, and their interactions in the unsteady burning process of the fuel bed are studied by formulating and solving a set of governing equations. Additional source terms in the governing equations are proposed to represent the transfer processes of mass, momentum, energy and gasified fuel between solid phase and gas phase of the porous bed. Also, porosity is introduced as a concept and an approach to express the blockage within the porous bed. Predicted speed of flame spread along the surface of the Heptane pool is around 2 m / s, which is close to experimental data. Flow field, isotherms and contours of mass fraction of fuel obtained have similar characteristics with typical experimental findings.