This paper presents a new numerical tool to model two-dimensional contaminant transport through unsaturated porous media using a meshfree method, called the Element Free Galerkin Method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The advection-dispersion equation with sorption is considered to illustrate the applicability of the EFGM. The Galerkin weak form of the governing equation is formulated using 2D meshfree shape functions constructed using moving least square approximants, which are constructed by using a weight function, a linear basis function and a set of non-constant coefficients. MATLAB code is developed to obtain the numerical solution. Two numerical examples are presented and the results are compared with those obtained from the finite element method. © 2008 Taylor & Francis Group, London.