In this paper,the ring shell lining with annularly verticalwalls made contact with the surrounding rock is considered as a combinationstructure formed of ring shell,inner and outer annular barrels on elastic fo-undation.The complex equation and its solutions of ring shell under deadload of lining and vertical and horizontal surrounding rock pressures are de-rived by the method of complex function.The governing equation and itssolution of the barrels on elastic foundation are also derived by theory ofcylindrical shell.And then,the ring shell lining is assembled by the subst-ructures by means of compatibility conditions of internal forces and defor-mations between them.In the paper,all formulas for the practical computa-tion in engineering are derived,the numerical examples are given and theeffects of the parameters of the lining on the work behaviours of lining alsoare discussed preliminarily