Knowledge of phase transformations in a hot stamping and cold die quenching process (HSCDQ) is critical for determining physical and mechanical properties of formed parts. Currently, no modelling technique is available to describe the entire process. The research work described in this thesis deals with the modelling of phase transformation in HSCDQ of boron steel, providing a scientific understanding of the process. Material models in a form of unified constitutive equations are presented. Heat treatment tests were performed to study the austenitization of boron steel. Strain-temperature curves, measured using a dilatometer, were used to analyse the evolution of austenite. It was found that the evolution of austenite is controlled by: diffusion coefficient, temperature, heating rate and current volume proportion of austenite. An austenitization model is proposed to describe the relationship between time, temperature, heating rate and austenitization, in continuous heating processes. It can predict the start and completion temperatures, evolution of strain and the amount of austenite during austenitization. Bainite transformation with strain effect was studied by introducing pre-deformation in the austenite state. The start and finish temperatures of bainite transformation at different cooling rates were measured from strain-temperature curves, obtained using a dilatometer. It was found that pre-deformation promotes bainite transformation. A bainite transformation model is proposed to describe the effects of strain and strain rate, of pre-deformation, on the evolution of bainite transformation. An energy factor, as a function of normalised dislocation density, is introduced into the model to rationalise the strain effect. Viscoplastic behaviour of boron steel was studied by analyzing stress-strain curves obtained from uni-axial tensile tests. A viscoplastic-damage model has been developed to describe the evolution of plastic strain, isotropic hardening, normalised dislocation density and damage factor of the steel, when forming in a temperature range of 600°C to 800°C. Formability tests were conducted and the results were used to validate the viscoplastic-damage model and bainite transformation model. Finite element analysis was carried out to simulate the formability tests using the commercial software, ABAQUS. The material models were integrated with ABAQUS using VUMAT. A good agreement was obtained between the experimental and FE results for: deformation degree, thickness distribution, and microstructural evolution.