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The propagation of the electromagnetic field inside a conducting slub extended in the infinity is treated by the use of a boundary element technique. The excitation is a current source arbitrarily oriented inside the conducting material. The conducting slub is situated in the air. The magnetic field intensity is expressed in terms of the electric vector potential T and the magnetic scalar potential Ω. The integral equations for these two field quantities are formed by the use of the Green’s function method into the original Helmholtz and Laplace equations for the T and Ω, respectively. Apart from the boundary conditions, the need of imposing at least one more additional condition between the field quantities becomes obvious during the solution procedure, with the help of a boundary element method. Examples are given using two materials with quite different electric properties, aluminum and graphite. The work can be extended in more complicated stratified media to face propagation problems in geometries with complex boundaries.