The effects of an external stress on the formation of ellipsoidal ω phase precipitates have been examined for a Ti-20wt%Mo alloy aged at 300°C. Application of a tensile stress accelerates the nucleation of ω precipitates but a compressive stress does not significantly affect it. Estimates of the average misfit strains along the loading and the transverse directions, based on the misfit strains of ω precipitates, from measurements of the length change and the lattice parameter reveal preferential formation of specific ω variants among crystallographically-equivalent four ones, which depends on the sense of the applied stress. This is supported by the result of the dependence of the number density of an ω variant on its misfit strain along the loading direction. This result, together with the dependence of the formation of ω precipitates on the sense of the applied stress, can be well understood through the interaction energy due to the presence of misfit strains between the applied stress and ω precipitate.