The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires complex programming skills beyond the ability of a typical undergraduate. In this article, we present a simple and systematic way of implementing the boundary element method for solving the Laplace's equation using MATLAB, a numerical software package commonly used in undergraduate courses. The examples will demonstrate that a package such as MATLAB serves well in introducing as well as implementing the boundary element method. (Contains 7 figures.)