This paper presents a numerical model of an integrated 3D casing-cement-formation system, to evaluate the mechanical tensile and shear failure of the cement at the casing-cement interface as the pressure and temperature conditions of the formation and borehole vary during production. The model which includes the formation pressure, unlike others proposed, was developed by stages under finite element discretization and compared to analytical models. Results show that increasing the formation temperature increases the probability of tensile and shear failure in the cement, while increasing the wellbore temperature decreases these probabilities. On the other hand, the decrease in the well pressure reduces the probability of shear failure and increases the tensile failure. In the case of formation pressure, the opposite occurs.