Finite element method is widely used to numerically simulate the seepage and the coupling of flow and stress in geotechnical engineering. In present，the finite difference method is the main numerical method of fluid flowing in porous media. Compared with the finite difference method，the finite element method is a valid numerical method and has more advantages than the finite difference method，but it is not deeply studied in solving reservoir problems. The flow equations for a single phase in an anisotropic reservoir and the equations of finite element method are established. Those equations are discretized in space by using Galerkin finite element method and in time by using backward difference method. Finally the linear equations are solved by Gauss-Seidel method. On base of the finite element equations and relative theory，eight-node quadrilateral elements are used，and a finite element simulating software is developed. For the unstable state flow of single phase fluid，the finite element method is compared with analytical solution for one-dimensional plane flow. And the radial flow in an anisotropic reservoir is simulated with the software package. The distribution of fluid pressure in formation and the production of the oil well in an anisotropic reservoir are obtained. It is shown that the finite element solution is precise enough compared with the analytical method，which proves that the provided method and program are correct，and that it is precise and reliable to solve reservoir problems with the finite element method. These researches can be used to guide the oil wells production，and present an important method to forecast the production output in oil reservoirs.