Aiming at geometrically nonlinear problems and using movement transformation as a point of departure, a global weak form integral equation was established from the virtual power principle on the basis of the S-R decomposition theorem and updated co-moving coordinate formulation. Numerical solutions were obtained by using element free Galerkin method (EFG). Usually, incremental and iterative methods are used to solve the nonlinear problems of numerical calculation. S-R decomposition theorem brings out a new strain tensor, which can reasonably reflect the state of stain and rotation on the condition of large displacement and large rotation, and are helpful in solving geometrically nonlinear problems. Numerical examples have shown that this method is reasonable and effective.