Young's modulus as well as tensile strength, ductility, fatigue life, fretting fatigue life, wear properties, functionalities, etc., should be adjusted to levels that are suitable for structural biomaterials used in implants that replace hard tissue. These factors may be collectively referred to as mechanical biocompatibilities. In this paper, the following are described with regard to biomedical applications of titanium alloys: the Young's modulus, wear properties, notch fatigue strength, fatigue behaviour on relation to ageing treatment, improvement of fatigue strength, fatigue crack propagation resistance and ductility by the deformation-induced martensitic transformation of the unstable beta phase, and multifunctional deformation behaviours of titanium alloys.