This paper presents two formulations for material discontinuity modeling in the element-free Galerkin method. The proposed methods involve an element-free Galerkin formulation in conjunction with two types of transformation methods which relate the nodal parameters and their corresponding physical nodal values to treat the material discontinuities in elastic bi-materials. The proposed methods eliminate the shortcomings of existing methods like Lagrange multiplier method, discontinuity enrichment method and penalty method typically used for material discontinuity treatment in element-free Galerkin formulations. Numerical examples show that the proposed methods yield accurate estimates of solutions.