In order to rationally impose essential boundary conditions in the element-free Galerkin（EFG） method,a hybrid element method coupling the radial point interpolation method（RPIM） and the EFG method is proposed.In this method,the problem domain is divided into two parts： one contains the essential boundary and is solved by the RPIM,and the other is solved by the EFG method;and,a coupling is performed according to the relationship between the two above-mentioned element-free interpolation methods.Numerical examples indicate that the proposed method is easy to program,and that it can concisely and effectively process the essential boundary condition,with a computation accuracy as high as that of the EFG method.