A method based on the fast Fourier transform was proposed to solve the generalized eigenvalue problems with multiple roots. This paper calculated dynamic responses on measure nodes with nonzero initial condition on one point. Both natural frequencies and mode shapes were extracted from data in the frequency domain. Responses under different initial conditions were calculated to get several sets of mode shape data. Taking cosine similarity of mode shapes as the discriminant parameter, multiple roots were identified. The numerical example shows that this method can identify the multiple roots efficiently and the result reaches a high accuracy.