This paper presents a meshfree modelling of two dimensional contaminant transport through saturated porous media using 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, two dimensional form of the advection-dispersion equation with continuous source is considered. The unknown concentration values are approximated by using moving least square approximants. 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. The results of the EFGM are compared with the analytical and finite element results and it is found that they match well. J. Ross Publishing, Inc. © 2009