Abstract: Introduces the principle of the EFGM (Element-Free Galerkin Method) and its application to steady state rolling process of slightly compressible rigid-plastic materials. The penalty function algorithm is utilized to meet the requirements of essential boundary conditions because the shape function of EFGM fails to satisfy conditions. To improve the accuracy, the tensor product weight function which has rectangular influence domain is picked out. The background cell in FEM is taken as integral element, and different Gauss integration schemes are used for the interior of solution domain and its boundary. The validity and correctness of EFGM are verified by comparing the results of actual plate rolling with that calculated via Rigid-Plastic FEM and experimental data in earlier works.