A group of substantially nickel-free beta-titanium alloys have shape memory and super-elastic properties suitable for, e.g., medical device applications. In particular, the present disclosure provides a titanium-based group of alloys including 16-20 at. % of hafnium, zirconium or a mixture thereof, 8-17 at. % niobium, and 0.25-6 at. % tin. This alloy group exhibits recoverable strains of at least 3.5% after axial, bending or torsional deformation. In some instances, the alloys have a capability to recover of more than 5% deformation strain. Niobium and tin are provided in the alloy to control beta phase stability, which enhances the ability of the materials to exhibit shape memory or super-elastic properties at a desired application temperature (e.g., body temperature). Hafnium and/or zirconium may be interchangeably added to increase the radiopacity of the material, and also contribute to the superelasticity of the material.