The classical panel method has been extensively used in external aerodynamics to calculate ideal flow fields around moving vehicles or stationary structures in unbounded domains. However, the panel method, as a somewhat simpler implementation of the boundary element method, has rarely been employed to solve problems in closed complex domains. This paper aims at filling this gap and discusses the numerical solution of the Laplace equation in bounded domains via the numerical panel method. It is shown that the panel method is an efficient and accurate computational algorithm for the solution of this class of problems. Several test cases in heat conduction and internal ideal flow are presented to show that the numerical panel method can be used in closed domains regardless of the complexities in the geometry and/or boundary conditions.