The superelasticity and shape memory effects upon torsional straining of samples of the binary titanium nickelide based alloy with the B 19' martensitic phase structure have been investigated. It has been found that, in samples plastically strained during their loading up to a specified torsional strain of ~39%, the superelasticity value can attain 6.3%, which is comparable with the classical superelasticity effect. The superelasticity manifestation in the martensitic state upon torsion straining of the samples has been compared with the results of similar studies on tensile straining of the titanium nickelide-based alloy samples.