Contaminants dispersed at the land surface migrate through the unsaturated and saturated porous media before reaching the groundwater. In order to ease and develop the practical way of contaminant transport simulation for complex geometry and boundary conditions, numerical formulations have been used extensively. In recent years, a group of new methods called meshfree methods have been developed; whose main aim is to eliminate structure of the mesh and construct approximate solutions for the discrete equation entirely in terms of a set of nodes. A limited amount of research is undertaken regarding the potential usage of the meshfree methods for modelling contaminant transport processes in the saturated and unsaturated porous media and in the area of landfill engineering. In view of the above aspects, in the present monograph, an attempt has been made to formulate a numerical model based on the meshfree techniques for modelling the migration of contaminants through the saturated and unsaturated homogeneous porous media and landfill liners. The monograph focuses on the work carried by the first author at Indian Institute of Technology Madras, India; as a part of his doctoral study.