We present a model of metallic plastic flow suitable for numerical simulations of explosive loading and high velocity impacts. The dependence of the plastic strain rate on applied stress at low strain rates is of the Arrhenius form but with an activation energy that is singular at zero stress so that the deformation rate vanishes in that limit. Work hardening is modeled as a generalized Voce law. At strain rates exceeding 109 s−1, work hardening is neglected, and the rate dependence of the flow stress is calculated using Wallace’s theory of overdriven shocks in metals [D.C. Wallace, Phys. Rev. B 24, 5597 (1981); 24, 5607 (1981)]. The thermal-activation regime is continuously merged into the strong shock limit, yielding a model applicable over the 15 decades in strain rate from 10−3 to 1012 s−1. The model represents all aspects of constitutive behavior seen in Hopkinson bar and low-rate data, including a rapid increase in the constant-strain rate sensitivity, with 10% accuracy. High-pressure behavior is controlled by the shear modulus, G(ρ,T), and the melting temperature, Tm(ρ). There are eleven material parameters in addition to G(ρ,T) and Tm(ρ). Parameters for Cu, U, Ta, Mo, V, Be, 304 SS, and 21-6-9 SS are provided.