Abstract: The exact relation between strain and displacement is given for nonlinear deformation of thin shell. The fundamental formula of large deformation when the deflection is on the same class with the thickness of the shell is derived after simplified rationally. The fundamental formula of large deformation when the deflection is on the same class with the length of the shell is derived exactly for cylinder shell deformed cylindrical shaped.

Key words: thin shell, nonlinear deformation, large deflection