Element-free Galerkin Method for the analysis of 2D geometrical nonlinearities is presented by means of geometrically nonlinear strain-displacement relation under small strain assumption.Due to the lack of Kronecker delta properties in meshless method,the penalty method is explored to enforce the essential boundary conditions.Results of numerical examples in geometrical nonlinearities have shown that element-free Galerkin method,with its high accuracy,is much more efficient to deal with these problems.