This chapter deals with finite difference method (FDM) with a focus on time-independent problems. It provides a difference scheme for solving the two-dimensional Poisson equation. The chapter briefly introduces both direct methods and iterative methods for solving a general system of linear equations, such as that resulting from the difference scheme for the Poisson equation. It discusses the error analysis of the difference method for solving elliptic equations. The chapter extends the construction of difference methods to some other elliptic problems, and presents an examplary MATLAB code for solving the Poisson equation.