Because of their excellent high temperature characteristics, Ni-based single-crystal alloys are used in applications where operating temperatures exceed 900ºC. The initiation of cracks under these conditions is generally associated with micro-scale porosities (typically between 10 and 20 microns). A rate-dependent crystallographic constitutive model in conjunction with a mass diffusion model has been used to study crack initiation in single crystal nickel-base superalloys, exposed to an oxidizing environment and subjected to mechanical loading. The time to crack initiation under creep and fatigue loading conditions has been predicted using a strain-based failure criterion. The problem has been solved using a two dimensional finite element analysis. A notched compact tension specimen has been studied with a casting defect, idealized as a cylindrical void, close to the notch surface. The analysis predicts that, due to the strong localization of inelastic strain at the void, a microcrack will initiate in the vicinity of the void rather than at the notch. The numerical results have shown that the time or number of cycles to crack initiation depends strongly on the applied load level and the void location. The coupled diffusion-deformation finite element studies have shown that environmental effects (i.e. oxidation) reduce the time or number of cycles to crack initiation, due to the oxidation-induced material softening in the vicinity of the notch and void.