This paper provides a new method to determine critical frequencies of any engineering structures by identification of peak frequencies of their internal damping loss factor curves. The novelty embodies the following aspects: first, the indirect method was applied to measure the critical frequencies of large complex thin-walled panels; second, the hybrid FEA-SEA was applied to analyse the sound insulation characteristics which provide an important approach to solve the middle frequency engineering problems. A hybrid of finite element analysis and statistical energy analysis was applied to calculate the dash sound transmission loss in the middle frequency range of 100∼2,000 Hz. A sound transmission loss experiment was conducted to verify the analysis. The trough of the sound transmission loss curve appeared at 200~250 Hz where the internal damping loss factor curve reached its peak. Therefore, the coincidence of the dash panel is proved to be at the critical frequency of 210 Hz.