Focusing on the porous square cylinder model, we employ numerical investigation to explore flow-induced vibration phenomena, influencing factors, and associated mechanisms. Initially, we provide a brief overview of the current research status regarding flow-induced vibration in porous media. Subsequently, we establish a porous square cylinder model and create grid divisions within STAR-CCM+. We conduct comparative analysis with existing research findings to validate the accuracy of the computed results in this study. By altering predefined parameters, we investigate the effects of changes in three influencing factors—porosity of the porous media region ε, the shape of the porous area, and additional sinusoidal motion within the porous area—on the fluid dynamics. This analysis yields flow field characteristics and lift coefficient curves under different conditions. Based on the computational results, we summarize general patterns of flow-induced vibration phenomena in porous column models, providing insights for further research on flow-induced vibration problems in porous media and their practical engineering applications.