Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh-based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advectiondominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two-dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using 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 EFGM employs moving least-square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. © 2009 John Wiley & Sons, Ltd.