The main objective of this paper is to study the influence of annealing heat treatment on the mechanical properties of the cold-rolled Interstitial Free Steel HC260Y and to characterize the fracture mechanisms of this material in its different states. Tensile samples were then cut in different orientations in accordance with the rolling direction. They were subsequently subjected to an annealing heat treatment followed by off-axis tensile tests. The main characteristics of cold-rolled and annealed specimens, in particular the hardening exponent and the Lankford coefficient, were compared. This study is based on a behaviour model that respects the structure of the material as well as its anisotropy. This model is represented by a behavior law, a hardening law and an evolution law. The fracture surfaces of different specimens were examined using the scanning electron microscope (SEM). The results indicate that the annealing treatment is an essential process for obtaining a steel with superior mechanical properties, suitable for industrial use mainly for deep drawing applications.