Observing the unique stress-strain curves of the superelastic shape memory alloy (SMA) in tension and compression, the primary intention of this study is to investigate the behavior of the shafts made of the same material, under torsional loading-unloading cycles for large angle of twist. Experiments have been performed for the superelastic SMA shafts with different unsupported lengths and angles of twist and the results are compared with those of stainless steel (SUS304) shafts under similar test conditions. As expected for the superelastic SMA, the residual strains are small enough after each cycle and consequently, the hysteresis under loading-reverse loading is much narrower than that for the SUS304. For large angle of twists, the torsional strength of the superelastic SMA increases nonlinearly and exceeds that of SUS304. Most interestingly, the slender solid superelastic SMA shafts are found to buckle when acted upon torsion for large angle of twist.