Abstract: Ceramic materials are prone to slow crack growth (SCG) which is stress and environmentally assisted. The kinetics of fracture being dependent on the load level, the temperature and the relative humidity, a thermally activated cohesive zone formulation was proposed and shown able to capture SCG [Romero de la Osa M., Estevez R., Chevalier J., Olagnon C., Charles Y., Vignoud L., Tallaron C., Cohesive zone model and slow crack growth in ceramic polycrystals, Int. J. Fract, 158(2): 157–167, 2009; Romero de la Osa M., Estevez R., Chevalier J., Olagnon C., Charles Y., Vignoud L., Tallaron C., Cohesive zone model for intergranular slow crack growth in ceramics: Influence of the process and microstructure, Modell. Simul. Mat. Sci. Engng., 19:074009, 2011; El Zoghbi B., Estevez R., Olagnon C., Modeling and numerical investigation of slow crack growth and crack arrest in ceramic polycrystals, Theor. Appl. Mech. Lett., 3(5): 13-051001, 2013]. In this paper, the calibration of the cohesive parameters for single crystals of sapphire and zirconia are presented and the characteristics of SCG in both single crystals are compared and discussed. Then, the intergranular SCG in ceramic polycrystals is considered with cohesive surfaces inserted along the grain boundaries. The influence of the microstructure in terms of the anisotropic elastic moduli, grain-to-grain misorientation and grain size effect are investigated. The effect of the initial stress state that originates from the ceramic processing on the kinetic of SCG and the level of the load threshold below which no SCG occurs is considered. SCG is grain size dependent with the decrease of the crack velocity at a given load level and improvement of the load threshold with the grain size. The initial thermal stresses are shown to be responsible for the grain size effect on SCG behaviour. The experimental results reported by A.H. De Aza et al. [De Aza A.H., Chevalier J., Fantozzi G., Schehl M., Torrecillas R., Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses, Biomaterials, 23: 937–945, 2002] show that the polycrystals of zirconia exhibits a higher resistance to SCG than the polycystals of alumina. Polycrystals of zirconia and alumina are both considered in this study. The failure kinetics, the role of the microstructure and the thermal stresses related to the processing are considered for both materials and the corresponding predictions are compared and discussed. Ultimately, the present description work aims at contributing to reliable predictions in long lasting applications of ceramics.