Titanium alloys are materials with exceptional properties including high specific strength, extreme corrosion resistance, and biocompatibility. Among them, metastable β titanium alloys are a prospective group exhibiting complex phase transformations which can be employed to improve the performance of the material. Microstructural mechanisms controlling phase transformations in these alloys are not completely understood. In this work, we propose a continuum-based model describing non-diffusional, displacive, reversible β → ω phase transformation which leads to a formation of stress-induced ω def phase. The proposed model utilizes a well-developed mathematical theory of martensitic phase transitions based on the Cauchy-Born hypothesis, and reformulates this theory to describe the crystallographic mechanism of β → ω def phase transformation. The model evaluates compatibility criteria at the interfaces between β and ω def phases in relation to the external stress and provides conditions for the formation of ω def phase.