The fracture of brittle coatings on a strained substrate is examined from two points of view. In the first case, the substrate deforms continuously and regularly spaced fractures occur in the coating. The spacingdat any strain &egr; is given by In &egr;/&egr;0= (4g/d) (1−d/d0), whered0, &egr;0are any convenient set of data points, andgis a parameter having the units of length. In the second case, the substrate deforms by crystallographic slip and fracture of the oxide may or may not occur at the slip step. The criteria for fracture are that the interface adhesive stresses be too large for the coating to sustain the necessary peel stress. Quantitative relations are given in terms of the coating thickness, fracture strain, and the orientation of the slip step with respect to the surface. The results for both cases are compared with experiment and found to be in essential agreement.