Abstract: The element-free Galerkin(EFGM)method is extended to solving the geometrically nonlinear problem. The EFG method is based on moving least square(MLS)approximations and the essential boundary conditions are imposed by the penalty factor method. Only nodal data are necessary and there is no need to make elements with nodes in this method. An incremental and iterative solution procedure using modified Newton-Raphson iterations is used to solve the geometrically nonlinear problem, and measurements of strain and stress are related back to the original configuration, namely, the total Lagrangian method is used. Examples show that in solving the geometrically nonlinear problem the element-free Galerkin method achieves results of good accuracy.