This paper aims at investigating the effect of vertical motion (or equivalently the effect of variable tensioning) of the floating unit on the vortex-induced vibrations of vertical risers. This is done using a numerical procedure, based on modeling assumptions, which, though simple, succeeded in describing some expected dynamic behaviors. The model simulates the riser dynamics using a finite element model coupled to a wake-oscillator model, of the van der Pol type, used to emulate the fluid dynamics. Vertical motion (or dynamic tension) is directly imposed to the top. The transverse amplitudes at each section feed the wake-oscillator, which responds with a transverse force that is applied to the riser. The rigidity matrix is updated at each time integration step. The analysis is also carried out with a commercial simulation code dedicated to riser analysis, with a similar wake-oscillator VIV module. Amplitude envelopes are extracted from the time series, showing response mode jumps. The application of the Hilbert-Huang spectral analysis technique helps distinguishing mode jumps by tracking frequency responses in time. The results of the two different dynamic models are compared with very good agreement.Copyright © 2007 by ASME