The paper presents a finite element mathematical model (FEM). This model describes operating and faulty states of the metal suspension on the basis of T-shaped embedded details of the tunnel lining located in the subway premises at the dynamic loading conditions. We considered the defect-free state of the metal details, the case of the destruction of the fixing T-shaped mortgage, the case of the complete corrosion of studs, the case of the partial corrosion of the right part of the upper stud. The mathematical model was verified using the experimental results. It is shown that FEM modeling makes it possible to establish the location of the characteristic points of a metal suspension, in which vibration accelerations should be measured to obtain objective data on its state. Using the developed mathematical model, we showed that to unambiguously determine the defective state of the metal details and determine the type of defect, it is necessary and sufficient to use a combination of spectral analysis, wavelet transform analysis and analysis of the acceleration vector hodograph. The results of experimental and numerical researches are presented.