Creep and damage of all oxide ceramic matrix composites were modeled by numerical methods. For pure tension, it was predicted that creep of polycrystalline alumina can be reduced by four orders of magnitude with unidirectional, 40 vol% single-crystal alumina fibers. Even lower creep rates were predicted for single crystalline YAG fibers. A significant reduction of creep rates is only predicted if off-axis loading of fibers is less than 20 degrees and the fiber-matrix interface is strong. A damage model based on the boundary element method was used to simulate the thermal shock resistance of CMCs with different fiber architectures and microstructures. Assuming a strong fiber-matrix interface, the model predicts brittle fracture and catastrophic failure for a low scatter of flaw size in the fiber and the matrix. The best damage tolerance for a CIVIC with weak fibers was predicted for a large scatter of flaw size for the matrix and a strong fiber-matrix interface. This design is compatible with high creep resistance.