Abstract: This paper gives the exact relations between strains and displacements for large deformation of elastic thin shells. The fundamental formula of large deformation, when the deflection is of the same order as the thickness of the shell, is derived based on rational simplification. The fundamental formula of large deformation, when the deflection is of the same order as the length of the shell, is derived exactly for cylindrical shell under cylindrical deformation. These formulas are in accord with practice and convenient to use. The exact solution of infinitely long circular cylindrical shell with one end fixed, the other end loaded by a couple is obtained. The approximate solution of infinitely long plane strip is obtained by the method of energy.