The relationship between THz wave and medium, as well as the transmission characteristics of THz wave are not only the basic topic in the THz technology research area, but also the critical evidence for the system designations of THz wave detection, imaging and non defective detection applications. As for the transmission problem of THz wave through medium, some models were constructed respectively for the homogenous medium and idea defective medium with the methods of system analysis, which was also motivated by the electromagnetic theory and some associated experimental results presented in some home and abroad literature references. The corresponding transmission functions were also deduced and presented. Finally, simulation experiments validated the effectiveness and reasonability of such models. The results follow the basic physical principles, and are consistent with the phenomenon observed in practical experiments. The conclusions made in this paper are meaningful for the deepened comprehension about the mechanism THz wave transmitting through medium.