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Variant selection of α (hexagonal close-packed, hcp) phase during its precipitation from β (body-centered cubic, bcc) matrix plays a key role in determining the microstructural state and mechanical properties of α/β titanium alloys. In this work, we develop a three-dimensional quantitative phase field model to predict variant selection and microstructural evolution during β → α transformation in Ti–6Al–4V (wt.%) under the influence of both external and internal stresses. The model links its inputs directly to thermodynamic and mobility databases, and incorporates the crystallography of bcc to hcp transformation, elastic anisotropy and defects within semi-coherent α/β interfaces in its total free energy formulation. It is found that, for a given undercooling, the development of a transformation texture (also called microtexture) of the α phase due to variant selection during precipitation is determined by the interplay between …