Management and quality control is one of the main issues in water resources management. Among the existing management methods, numerical modeling and simulation of groundwater resources using computer programs is one of the most economical and applicable methods. One of the recent developments in this field is the application of mesh less methods that does not need mesh generation and unlike other conventional numerical methods does not have any problem in dealing with irregular geometry in boundaries. One of the most powerful mesh free methods is the finite point method. Application of finite point method in many fields has been investigated. This shows that this method could offer economical and precise solution. The main objective of this research is to investigate the application and performance of finite point method in modeling of contaminant traort in ground water resources. In developing the model a new form of weight function is used, which is sensitive to both distance and direction. This will improve the results. Differential equations of the hydraulics and pollution traort were developed as the first step using finite point methods. After developing the algorithms a computer program was constructed using C++. The program solves the hydraulics and contaminant traort simultaneously. In the first step hydraulics is determined at time t and then this information is used to solve for the contaminant traort. The program has the capability of solving ground water flow and contaminant traort in one and two dimensions. Results obtained for case studies showed that the method has good convergence and precision in contaminant traort problems. For example, in 2 D case for ground water flow, comparison of the results with finite difference method shows 1.5 to 4 percent difference. For 1 D case for contaminant traort, comparison of results with analytical solutions shows a difference of 1-4 percent.