The aero-engine casing is a key component for carrying loads. With the purpose of improving the thrust-weight ratio of the aero-engine, the casing is required to be designed to be as thin as possible. Therefore, the vibration of aero-engine's rotor, support, and casing will be easily coupled causing the whole engine's vibration to be more serious. Considering the structural vibration propagation is essentially the vibration energy transmission, the structural intensity (SI) method is popular and widely used to investigate the transmission phenomena of vibration energy in vibrating structures. This method combines forces with velocities to quantify the vibrational energy flow (VEF) transmitted in the structures by its directions and magnitude. Therefore, the SI fields are quantified by the developed computation system which combines the finite element design language and the in-house code. And a model of dual-rotor–support–casing coupling system subjected to the unbalanced forces of the rotors is established in this paper. The scalar and vector diagrams of instantaneous SI fields are visualized to show the main vibration energy transmission paths among these three parts. Moreover, the relationship between the SI and the mechanical energy is derived from the kinetic equation. According to this relationship, the phenomenon that the vibration energy and the strain energy are always converted to each other in the middle part of the rotor shaft with the first-order bending mode is discussed, which reveals the cause of the first-order bending mode of the rotor from a microscopic point of view.