Abstract: An EFGM(Element Free Galerkin Method) based algorithm is developed to solve axisymmetric problems in this paper.Formulation is established via a conventional weighted residual technique.Numerical examples of reinforced concrete pipes are studied to validate the proposed approach.Both elastic and visco-elastic cases are taken into account.For the case of viscoelasticity,a self-adaptive precise algorithm in the time domain is employed.Satisfactory results are obtained in terms of convergence rates of displacement and stress,agreeing with other solutions.