This work compares mechanical behaviour of alpha, alpha+beta and beta titanium alloys in a range of strain rates from 0.001 to 1000 1/s and stress triaxiality (0.3-0.6) at room temperature. Specimens of titanium alloys were studied under tension using an Instron VHS 40 / 50-20 servo hydraulic test machine. Analysis of stress state and strain distribution in smooth and notched samples under tension was carried out by computer simulation. The damage accumulation model, complemented with phenomenological laws for voids nucleation, growth and coalescence, was adopted for describing the fracture process of single and multiphase titanium alloys. It was shown that stress triaxiality is important for prediction of damage evolution and fracture of titanium alloys at high strain rates. It was obtained that strain localization phenomena play a major role in the fracture process at lower triaxiality factor. It is found that the strain to fracture of titanium alloy is strongly depended on the stress triaxiality and strain rate above 100 s-1. The strain to failure of alpha titanium alloys at room temperature decrease by 3.7 times with increasing stress triaxiality from 0.3 to 0.6 in wide range of strain rates.