A physically-based model for the deformation of Ti-6%-Al-4%V is proposed. The various deformation mechanisms active in this material over the whole range of temperatures of industrial interest are discussed, and a strategy by which the relevant strengthening effects are captured in the model is proposed. The flow stress contains a thermal and an athermal component. The thermally activated processes are modeled based on the Kocks-Mecking formalism, while the athermal processes are simulated using an internal state variable. The deformation of the α-and β-phases is captured separately. The model is calibrated based on experimental results obtained from tests performed in the temperature range (77-1400 K) and at strain rates between 10 - 3 and 10 s - 1 . The model predictions are extrapolated to strain rates as high as 2000 s - 1 . The experimental findings are presented in the companion paper.