This work presents an advanced crystal plasticity model for the simulation of the mechanical behavior of multiphase advanced high-strength steels. The model is based on the Visco-Plastic Self-Consistent (VPSC) model and uses information about the material’s crystallographic texture and grain morphology together with a grain constitutive law. The law used here, based on the work of Pantleon, considers how dislocations are created and annihilated, as well as how they interact with obstacles such as grain boundaries and inclusions (carbides). Additionally, strain rate sensitivity is implemented using a phenomenological expression derived from literature data that does not require any fitting parameter. The model is applied to the study of two bainitic steels obtained by applying different heat treatments. After fitting the required parameters using tensile experiments in different directions at quasi-static and high strain rates, formability properties are determined using the model for the performance of virtual experiments: uniaxial tests are used to determine r-values and stress levels and biaxial tests are used for the calculation of yield surfaces and forming limit curves.