Based on the principles of virtual work for continuum medium, the element free Galerkin method to simulate the numerical calculations of steady-state creep was used and the discrete equation was derived in meshlss method for steady-state creep. The es-sential boundary conditions and volume incompressible conditions can be realized by em-ploying the penalty parameters, so the symmetric positive definite system stiffness matrix can be yielded. Results of numerical cases show that element free Galerkin method, with its high accuracy, is much more convenient to deal with the pre-process and post-process, the results by meshless method is in good agreement with the exact solution data.