Abstract：Based on analyzing the micro critical seepage phenomena of gas-liquid two-phase flow in a single fracture，a random and compound mathematical model was constructed to describe this phenomenon. Using this model，the numerical simulations of the probability distribution scope of the occurrence of critical seepage phenomena，the micro characters of gas/water connected clusters in critical seepage district，and the characteristics of the pressure gradient in critical seepage district are all carried out. The mechanism of the gas-water two-phase critical seepage law is revealed；and the critical seepage phenomena could occur when the relative gas saturation is 44%–77%；but the probability of the occurrence of the phenomenon is above 0.8 when the gas relative saturation is 47%–65%. However，when the gas relative saturation is 57%–60%，the probability of the occurrrence of the phenomena is 1.0.
