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Dual phase (DP) steels consisting of two phases, ferrite and dispersed martensite, offer an attractive combination of strength and stretchability, which is a result of the strong distinctions of these constituents in mechanical properties. However, the damage behavior in DP steels exhibits a rather complex scenario: voids are generated by the debonding of the hard phase from the matrix and the inner cracking of the hard phase in addition to by inclusions. The target of this study is to describe the initiation and evolution of damage in DP steel and develop a microstructure-based model which is capable of reflecting the underlying damage mechanisms. Both uniaxial and biaxial tensile tests are performed and the subsequent metallographic investigations are executed to reveal the mechanisms of damage initiation and evolution under different stress state condition and attention will be paid on the influence of various microstructural features on the initiation of damage. In finite element (FE) simulations, the microstructural features are taken into account by the representative volume elements (RVE). Different treatments of the constitutive behaviour of each constituent including isotropic hardening rule and crystallographically dependent configuration with crystal plasticity finite element method are investigated. Several numerical aspects are also discussed, such as RVE size, mesh size, element type, and boundary connections. In the end, the study is attempting to achieve a quantitative assessment of the cold formability of the investigated steel in a microscopic level based on microstructure information of material as well as to understand the damage mechanisms under different stress states condition which cause the macroscopic failure during plastic deformation.