The specific case of the differential Maxwell system in the rectangular coordinates is considered as the basic mathematical model of electromagnetic wave propagation in the spatial guided structures. The general wave PDE (partial differential equation) is got including all scalar components of the electromagnetic field vector intensities. Equivalence of this PDE to the original Maxwell statement is proved. Mathematical simulation of the electrodynamic phenomenon is done using boundary value problem regarding the aforesaid wave equation. This problem is solved explicitly. The obtained exact formulae are used for numerical implementation and computer modeling of the considered engineering process.