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Based on the non-linear air leakage seepage equation for an anisotropic porous medium, on the seepage diffusion equation of multicomponent gas and on the seepage synthetic heat transfer equation of a porous medium, the numerical model for field flow problems of irregular patterns of a goaf with multiple points of leaking air is established and simultaneously solved by the upwind mode finite element method (G3 computer program). According to the complexity of irregular patterns of a goaf with multiple points of leaking air, the flow pattern in a large area of such a goaf and the variation in gases of methane, oxygen and CO and in temperature are theoretically described. In the calculation, the goaf is regarded as a caving anisotropic medium and the coupling effect of methane effusion on spontaneous combustion is considered. The simulation results agree well with practical experience. In addition, the spontaneous combustion process is also simulated, indicating that 1) the spontaneous combustion often takes place near the area where fresh air leaks in and 2) the fire sources can be classified into static and dynamic zones. Therefore, in practical fire preventing and extinguishing, we should clearly distinguish the upstream air leaking points from the downstream ones in order to take proper measures for leakage stopping.