The complex behavior of the aquifer system is studied by solving a set of governing equations using either analytical or numerical methods. Numerical techniques like finite difference method (FDM) is being used to solve differential equation in some simple cases. Recently Meshless methods are developed in engineering fields. They are used for solving differential equations in both simple and complex cases. As this methods needs no meshing or re-meshing on the domain the shortages of meshing disappeared. Less studies already performed in groundwater flow modeling with meshless method. In this study Meshless local Petrov-Galerkin with moving least squares approximation function and spline weight function is used to model groundwater flow in Birjand unconfined aquifer in steady condition. The computed surface of groundwater with meshless local Petrov-Galerkin method is compared with the results observation. The results are found satisfactory. The relative mean error and root mean square error of computed groundwater surface from Meshless Local Petrov-Galerkin are 0.0002 and 0.483 respectively.