The radial displacement of the soft rock roadway has great influence on the coal mine production. Based on double yield surface model,using the conventional triaxial test data of a mudstone,the loading surfaces which were ex- pressed by the first and the third main plastic strain(ε1p ,ε3p ) as the hardening parameter were fitted. According to the verified hypothesis of complete loading,the non-associated flow rule of the mudstone material was derived,and the sur- rounding rock plastic zone scope and radial displacement solution were obtained. The results show that:① the form of two loading surfaces of the mudstone material are quadratic function,and the coefficients can be expressed as a linear function of ε1p or ε3p ,and the value of the plastic strain increment component is determined. ② the derived non associ- ated flow law contains a constant term,the reason is that in the process of loading,it will first reach the loading surface of the ε3p ,when ε1p happens to be 0,ε3p is the value of the constant. ③ in this paper,the authors consider the rock char- acteristics of strain nonlinear softening,rule out the subjective cognition of “assumed flow rule” and others,get the an- alytical solution of the range of plastic zone and radial displacement,obtain the linear fitting formula between the range of plastic zone,radial displacement and excavation radius under the condition of constant stress.