An Element Free Galerkin "EFG# method based formulation for steady dynamic crack growth in elasticÐ plastic materials is developed[ A domain convecting parallel to the steadily moving crack tip is employed[ The EFG methodology eliminates the stringent mesh requirements of the Finite Element Method "FEM# for such problems[ Both rate!independent materials and rate!dependent materials are considered[ The material is characterized by von Mises yielding condition and an associated ~ow rule[ For rate!independent materials\ both the in~uence of crack speeds and that of strain hardening on the mechanics of steady dynamic crack growth are investigated[ For rate!dependent materials\ only a non!hardening material is considered with emphasis on determining the in~uence of viscous properties of materials and crack speeds[ The in~uence of strain hardening on steady dynamic crack growth shows the same trends as for steady quasi!static crack growth[ The simpli_cations used in the literature in deriving analytical solutions for high strain!rate crack growth have been examined thoroughly using the numerical results[ Þ 0887 Elsevier Science Ltd[ All rights reserved