The mechanical model of circular layer-crack structure of coal heading face is established with the simplification that the laneway is circular. Based on the expression of total potential energy function
a fold catastrophe model of circular layer-crack structure is established; the sudden change condition of gas outburst is given. The research results indicate that the coal and gas outburst will happen if pressure drop of the two sides of plate is larger than critical value. This research result is useful for gas outburst prevention.