This chapter introduces the boundary element method by presenting its application to a problem such as bending of prestressed elastic membrane subjected to a distributed pressure. The Laplace equation governs this problem and, due to its simplicity, allows us to illustrate the application of the boundary element method step by step. The purpose of this chapter is to know the steps for applying the method to the solution of the governing equation that governs the problem. How the integral equations of this equation are obtained from this equation, how these equations are discretized using BEM, and how the numerical solution of the problem is reached. This chapter then presents the general methodology of analysis that will be used in the book.