The mechanical anisotropy of low carbon steel sheets, usually characterized by the Lankford parameter, is strongly correlated to the crystallographic texture and its evolution during deformation. In this study, a homogenization model based on crystal plasticity was employed to simulate the evolution of the Lankford parameter during tensile deformation of three different steel alloys commonly used in the automotive industry. The crystallographic texture, together with other material parameters, is used as an input for the model, whereas the calibration procedure is only carried out on the experimental tensile test data of the samples aligned along the rolling direction of the sheet. The validation of the model is then performed on the experimental data of tensile samples oriented along 45° and 90° with respect to the rolling direction of the sheet. Despite the relative simplicity of the model, the simulations were able to capture not only the absolute value of the Lankford parameter, but also the evolution of this parameter during the tensile deformation.