The aim of this paper is to design the mathematical model of groundwater flow. Groundwater is not static, it flows in an aquifer and its flow can be described using partial differential equation and associated initial-boundary conditions. The work considered three dimensional steady state groundwater flows. Then the model of groundwater flow in discharging an aquifer at a well and the flow of water under a dam solved using the Laplace homotopy perturbation method, the paper focused on groundwater flow under a dam and in discharging an aquifer at a well.