The multimode vibration characteristics associated with slender marine risers/pipes are widely seen in the case of complex marine environments. Firstly, by using a two-way fluid-structure interaction technique, numerical simulations were performed on the vortex-induced vibration of a flexible marine riser model subjected to shear and uniform flows. Secondly, based on the analysis of position-frequency-energy spectra, the multimode characterized vibration along the pipe span was investigated. Then, an empirical mode decomposition technique called FB-EMD, based on the Fourier transform and band-pass filter, was used to adaptively decompose the vibration data into some intrinsic mode functions. By analyzing the time-frequency characteristic information, the transient evolution characteristics of the vibration modes associated with the flexible riser model were then discovered. It is found that the phenomena of multimode vibration along the slender flexible pipes are quite common. With the increase of flow velocity, higher order vibration modes are continuously triggered, and with the energy transfer between modes, the apparent modes at different periods compete fiercely, often resulting in transient multimode coexistence. The time-frequency-energy Hilbert spectral analysis shows that the random and natural vibration modes caused by the combined effects of local vortex shedding and energy transfer from adjacent pipe sections are excited in a wide frequency band, and the energy of each dominant vibration mode is usually time-varying.