Using the Gleeble 1500, incremental and continuous hot compression tests, simulating hot rolling, were performed on C‐Mn, Nb‐T, and Nb steels with test temperatures varying between 875 and 1100°C and strain rates between 0.5 and 20 s−1. Four models are proposed. The stress peak model allows the prediction of continuous stress‐strain curves from incremental curves and vice versa through the use of stress restoration index K. Variation in K for Nb‐T1, C‐Mn and Nb steels at strain rates of 3, 12 and 20 s−1 was found to be negligible. The predicted stress strain curve corresponds to experimental stress strain curve at same temperature and strain rate. The strain history model predicts continuous strain‐time curves from incremental stress‐strain curves using ‘constant’ ‘negative strain’ restoration index. At 950°C, with holding time 2 s and strain rate 12 s−1, strain time decay curves obtained for C‐Mn, Nb and Nb‐T, steels were ε = 1.5e−05t, ε = 1.2e−0.36t and ε = e−0.3t, respectively. The creep model analysis relates creep strain rate to the testing strain rate. For Nb steel at 875°C, and test strain rate of 12 s−1, ∊creep was found to be 9.5 s−1. The stress history model predicts continuous stress‐time curves from incremental stress‐time curves. Stress decay curve for C‐Mn steel at 1100°C and ∊ = 3s−1 was found to be σ = 181e−0.04t. Hot rolling characteristics of steels can be accurately predicted using hot compression tests and proposed models.