It is developed a method for the determination of the longitudinal component of the electric field generated by a surface current density in the interior or the exterior regions. The proposed method is based on the dyadic Green´s function of the region under consideration, beeing analysed interior regions, assuming the knowledge of the analytical solution for the scalar wave equation in the orthogonal coordinate systems and external regions, using spherical and cylindrical coordinate systems. For the each solution, it is shown the convergence of the expression obtained for the longitudinal component of the electric field. Based on the developed method, a model of analysis is elaborated to determine the field and the characteristics impedance of coaxial cables of arbitrary cross section. The model is applied to cables with circular and rectangular sections. The dyadic Green´s function method is finally applied to the analysis of coaxial cables with internal metallic struts periodicaly placed.