In order to enhance the vibration isolation effectiveness of airborne equipment vibration isolation systems and optimize their layout, a typical vibration isolation system is examined as a case study. The coordinate transformation method is employed to establish the differential equation of motion for the vibration isolation system. System modal characteristics are calculated using MATLAB software and compared with results obtained from ANSYS simulations. Additionally, the impact of various layout parameters on the system modes is analyzed. The coordinate transformation method facilitates an accurate calculation of the modal properties of the vibration isolation system. Once layout parameters such as arrangement height and horizontal distance are established, the natural frequency ratio in the horizontal direction can be determined. It is observed that an increase in arrangement height leads to a decrease in horizontal frequency while simultaneously increasing the horizontal frequency ratio; however, variations in arrangement height do not influence vertical frequencies. Furthermore, it is noted that greater horizontal distances correspond to higher natural frequencies in that direction; conversely, this distance does not affect natural frequencies along other axes. Thus, layout parameters—including arrangement height and horizontal spacing—significantly influence the vibrational modes of the system. It is recommended that the layout dimensions of vibration isolators be fully considered during the initial design phase of airborne equipment, to prevent the installation size parameters from affecting the vibration isolation effect.