The response characteristics and suppression of flow-induced vibrations of rectangular prisms with various width-to-depth ratios were experimentally investigated. The prisms were rigid and elastically mounted at both ends to enable constrained torsional vibrations only. The present study focused on torsional vibrations, one of the three types of flow-induced vibrations generated in a rectangular prism. First, the response characteristics of torsional vibrations generated in rectangular prisms were investigated by free-vibration tests. It was found that the response characteristics of torsional vibrations generated in rectangular prisms could be classified into six patterns depending on the width-to-depth ratio. Next, the response characteristics of torsional vibrations observed in the free-vibration tests were reproduced by forced-vibration tests, and the mechanisms by which the three types of flow-induced vibrations, low-speed torsional flutter, vortex excitation and high-speed torsional flutter, are generated in the rectangular prisms were elucidated on the basis of characteristics of fluid forces and visualized flow patterns. Experiments were also carried out to establish an effective method for suppressing flow-induced vibrations generated in the rectangular prisms, and it was found that low-speed torsional flutter and high-speed torsional flutter could be suppressed by placing a small normal plate upstream of the prism, which results in suppression of the alternating rolling-up of the shear layers separating from the leading edges of the prism. It was also found that vortex excitation could be suppressed by placing a splitter plate downstream of the prism, which results in suppression of the generation of wake vortices.