Abstract: On the basis of stability theory and the analytical solutions of thick-walled cylinder of elasto-plastic material, the post-yield equibrium path of shaft excavation is tracked and adopted to stability analysis of the surrounding rock. The results show that the instability of surrounding rock and the occurrence of rockburst depend not only on the post-peak property of stress-strain total curve of rock material, but also on the type of equilibrium path curves during excavation of shaft. The equilibrium path curve describes the post-yield behaviour of the structure of surrounding rock, and can only be classified into two types. A point on the curve of one type is corresponding to a stable stage of the equilibrium, which accumulates plastic deformation but the instability not occurs. The other type is related to limit-point-type instability and displacement snap-through. The equilibrium path curve of shaft excavation is a key factor of inducing rockbursts of surrounding rock. The limit-point-type instability and displacement snap-through are possible mechanism of rockbursts in homogeneous rock.