In Concrete-Faced Rockfill Dams (CFRDs), the role of impermeability of concrete face is a key factor on the dam design. Dam body and concrete face slabs deform as a result of reservoir impoundment and the crest settlements. Concrete face deformation leads to development of excess tensile and compressive stresses in the face, while perimetric joint opening is also possible. Development of high value stresses in concrete face can lead to face slab cracking and leakage of reservoir water. Perimetric joint opening is also one of the most important factor in reservoir water leakage. In this thesis, the effect of different geometric parameters, dam body material characteristics and interface behaviour between concrete face and cushion layer in the static condition and effect of reservoir water loading, slab thickness, earthquake acceleration, dam body material characteristics and dam height in the dynamic condition on dam body deformation and specially concrete face behaviour, have been studied. The nonlinear behaviour of rockfill is modeled using Modified Drucker-Prager Cap Plasticity constitutive model, while linear elastic model is adopted to simulate the concrete face behaviour.2D finite element static and dynamic analyses, have been performed employing ABAQUS software.Analyses results indicated that the most part of deformations in dam body and concrete face occur as a result of reservoir impoundment. Having reservoir filled up, the face slab out of plane deformations increas and the tensile and compressive stresses start to be develop at the toe and midlength of the face slab, respectively.The most important factors in CFRD performance could be referred to dam height and material characteristics of dam body in the main zone. Having the height of dams increased or the body matterial stiffness decreased the tensile stresses of concrete face at the toe will be increased. Another words, the growth of face slab out of plane deformations, results more tensile stresse and an increase to perimetric joint opening. However, it is not essentially a case in the case of compressive stresses induced in the face slab. In full reservoir condition while CFRD is subjectes to earthquake loading, high value of stresses develop in the concrete face. For the dynamic response, earthquake acceleration, dambody material characteristics and dam height, are of the important factors affecting on stresses in the concrete face. The effect of various parameters on developed stresses somewhere 40 percent face length close to dam crest, are not significant, exceptional in case of dam height and face slab thickness parameter analyses. It is concluded that maximume stresses in the concrete face slab are expected to occur somewhere around 10 to 40 percent of face slab length, measured from slab toe.