This paper presents an alternative numerical method to model the two-dimensional contaminant transport through saturated porous media using a meshless method called Element Free Galerkin Method (EFGM). In EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no elements or characterization of the interrelationship of the nodes is needed to construct the discrete equations. For analysis, the two-dimensional advection-dispersion equation with sorption is considered. The unknown concentration values are approximated by using moving least square approximants, which are constructed using a weight function, a linear basis function and a set of non-constant coefficients. A weak form of the governing equation is formulated and Lagrange multiplier method is used for enforcing the essential boundary conditions. MATLAB code is developed to obtain the numerical solution. Two numerical examples are presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the finite element method. Copyright ASCE 2008.