<p>The Vortex Self-Induced Vibration (VSIV) is a complex phenomenon, less explored than the traditional Vortex Induced Vibration (VIV), and its understanding is very important to be discussed and analyzed to determine the riser-fluid interaction on deep waters for the oil &amp; gas industry. It may represent an additional source of fatigue in the riser design when the Floating Production Unit (FPU) imposes vertical motions at the riser top, caused mainly by the wave action, inducing vibrations in the riser plane, causing vortex-shedding and provoking oscillatory motions out of the riser plane. To deal with fundamental aspects of such a rich phenomenon, a numerical assessment of experiments with an elastically mounted cylinder exposed to an oscillating flow is carried out in the present paper. To this end, the experiments conducted by Sumer and Fredsøe were used as reference. For the numerical simulations, two types of models were investigated: one based on Computational Fluid Dynamics (CFD), the Discrete Vortex Method (DVM), and other based on a semi-empirical method, the Phase Synchronization Method (PSM), both in two-dimensional domains. Several parameters involved in DVM and PSM models need to be calibrated, and some of them are discussed in this paper. In principle, it is important to highlight that both numerical approaches were not developed for the purpose of application of prescribed motion, but for the classical VIV phenomenon, with a constant current, becoming challenging to reproduce numerically the experimental results. Besides, comparisons on scaled models are very challenging to be reproduced numerically, and another point raised in this paper is how to perform the numerical and experimental post-processing of time series to generate comparable results of relevant aspects of the phenomenon. This study represents a first step towards applying the DVM or PSM methods on risers in full scale and with different types of configurations.</p>