A methodology is proposed to estimate creep rupture life for advanced ceramics such as continuous fiber reinforced ceramic matrix composites (CFCMC). Based on the premise that the damage pattern takes the form of a heterogeneous distribution of grain boundary cavities in the majority of creep life, a damage parameter is incorporated in various creep strain rate equations. The resulting constitutive equations for creep strain and accumulated damage are cast in terms of stress, and other affinities. It is pointed out that these affinities can be derived from a scalar creep potential in nonequilibrium thermodynamics. The evolutionary laws are formulated based on many micro-mechanical models. The time-dependent reliability or hazard rate for a Sic is then established by damage mechanics with Weibull analysis. A unit cell model is presented for predicting life of a uni-directional CFCMC subjected to a constant far-field stress. A system of coupled first order ordinary differential equations is derived from which the evolution of creep damage can be solved giving the rupture life. It is shown that the stress dependence on the lifetime is very sensitive to the type of damage mechanisms active at the microstructural level.