The behavior of the yield strength of steel and a number of aluminum alloys is investigated in a wide range of strain rates, based on the incubation time criterion of yield and the empirical models of Johnson-Cook and Cowper-Symonds. In this paper, expressions for the parameters of the empirical models are derived through the characteristics of the incubation time criterion; a satisfactory agreement of these data and experimental results is obtained. The parameters of the empirical models can depend on some strain rate. The independence of the characteristics of the incubation time criterion of yield from the loading history and their connection with the structural and temporal features of the plastic deformation process give advantage of the approach based on the concept of incubation time with respect to empirical models and an effective and convenient equation for determining the yield strength in a wider range of strain rates.