The inventive titanium alloy comprises, expressed in mass %: aluminium 4.0-6.3; vanadium 4.5-5.9; molybdenum 4.5-5.9; chromium 2.0-3.6; ferrum 0.2-0.5; the rest being titanium. An equivalent molybdenum content is determined as corresponding to Mo.sub.equiv.gtoreq.13.8. The inventive method for heat treatment consists in heating to t.sub..beta..revreaction..alpha.+.beta.-(30-70).degree. C., conditioning during 2-5 hrs, air or water cooling and age-hardening at a temperature ranging from 540.degree. C. to 600.degree. C. during 8-16 hrs. Said alloy has a high volumetric deformability and is used for manufacturing massive large-sized forged and pressed pieces having a high strength level, satisfactory characteristics of plasticity and fracture toughness.