Abstract: In order to study the surrounding rock stability of deep rectangular roadway, using the conformal mapping function of complex variables function, the rectangular holes on ξ plane are mapped as unit circle of z plane. Through the method of elastic mechanics, rectangular puckering problem is simplified as stress problem around the inner hole in infinite domain; combining with Christopher balding joule-thomson viscoelasticity model, a deep rectangular roadway surrounding rock stress distribution is drawn. Studies show that the stress state change of rectangular roadway surrounding rock has direct relationship with the aspect ratio of rectangular roadway and pressure coefficient; and using mathematical software mathematic, stress distribution around working face can be seen intuitively by graphical expression.