Mathematical modelling is used to study the evolution of damage caused by indentation loading on curved bilayers consisting of brittle shells filled with polymer support material. Such loads are pertinent to all-ceramic crown structures on tooth dentin in occlusal function. The aim is to develop tools to assist in the design of such structures to ensure both high damage resistance and high damage tolerance. Specifically, the initiation and propagation of a radial crack emanating from the interface is studied using the boundary element method (BEM) in three dimensions. The system that is analysed consists of a spherical indenter and both flat and convex bi-material samples. A semi-circular intrinsic flaw/crack is assumed to lie on the axis of indentation at the interface of the two materials, in the coating. Upon application of an indentation load, the mode I stress intensity factor distribution along the crack front is determined and the crack front is propagated using a small increment. By repeating this process, the critical load for propagation of the crack is obtained as a function of crack size. The results compare well with experimental crack propagation studies in bi-materials, as well as observed damage in porcelain crowns that have been used to repair teeth. The convex models show that radial cracks can exist in the brittle coating, without leading to catastrophic failure, up to a critical crack length. An increase in the applied load, causing the crack to grow beyond this length, causes the coating to fail in an unstable way. The results show that there is an optimum combination of design parameters for maximising the damage resistance. It is shown that larger convex radii of curvature lead to higher damage tolerance. (C) 2006 Elsevier Ltd. All rights reserved.