An aquifer is a layer of porous substrate that contains and transmits groundwater. When water can flow directly between the surface and the saturated zone of an aquifer, the aquifer is unconfined. The deeper parts of unconfined aquifers are usually more saturated since gravity causes water to flow downward. A confined aquifer is an aquifer that is overlain by a relatively impermeable layer of rock or substrate such as an aquiclude or aquitard. If a confined aquifer follows a downward grade from its recharge zone, groundwater can become pressurized as it flows. This can create artesian wells that flow freely without the need of a pump and rise to a higher elevation than the static water table at the above, unconfined, aquifer. Groundwater is a highly useful and often abundant resource. However, over-use, or overdraft, can cause major problems to human users and to the environment. The most evident problem (as far as human groundwater use is concerned) is a lowering of the water table beyond the reach of existing wells. Wells must consequently be deepened to reach the groundwater; in some places (e.g., California , Texas and India ) the water table has dropped hundreds of feet because of extensive well pumping. In the Punjab region of India, for example, groundwater levels have dropped 10 meters since 1979, and the rate of depletion is accelerating. A lowered water table may, in turn, cause other problems such as groundwater-related subsidence and saltwater intrusion . Water pollution of groundwater, from pollutants released to the ground that can work their way down into groundwater, can create a contaminant plume within an aquifer. Movement of water and dispersion within the aquifer spreads the pollutant over a wider area, its advancing boundary often called a plume edge, which can then intersect with groundwater wells or daylight into surface water such as seeps and springs , making the water supplies unsafe for humans and wildlife. The interaction of groundwater contamination with surface waters is analyzed by use of hydrology traort models . In November 2006, the Environmental Protection Agency published the Ground Water Rule in the United States Federal Register. The EPA was worried that the ground water system would be vulnerable to contamination from fecal matter. The point of the rule was to keep microbial pathogens out of public water sources The 2006 Ground Water Rule was an amendment of the 1996 Safe Drinking Water Act. One of the most important matters that face to human is the management of quality and quantity of water's sources. One of the economical and useable procedures for expecting the future by solves the model with computer is numerical modeling of aquifer and the simulation of situation. As a considerable method between the numerical models is the method with good stable characteristics, high velocity about the analysis of information and with so much accuracy in expecting the situation of aquifer. One of the most potential methods is power series that we can achieve our aims. The main goal of this thesis is considering the efficiency of power series about the quality modeling of underground waters. At first the differential equations that they are used in hydraulic of underground waters by power series convert to algorithm and then considering the treatment of models quality about leaking of pollutions in underground waters is achievable. Of course we perform this operation by solving the differential equation, use boundary condition and write a good algorithm according to same method. Then according to algorithms, we able to develop a program with C++ language. The conclusions of modeling operation are compared with analysis solving methods and definite components about velocity and accuracy.