The effects of complex geometry on contact damage in bi-layer systems composed of curved brittle coating layers on compliant polymeric substrate is investigated. Previous studies of this problem utilise relatively simple flat or singly curved (domed) model structures. It is not known the extent to which conclusions driven from such observations may extended to more complex (practical) geometry. Glass plates of 1000 mu m thick are used as representative of the brittle coating layer, and epoxy filler under layer as representative of under layer support. A series of doubly curved specimens (having curvatures of 4 and 8mm) are produced to allow investigation of the influence of complex curvature on the evolution of damage. The specimens are tested by indentation with spheres of 4 mm radius loaded along the convex axis of symmetry. For comparison, some specimens loaded parallel to the axis of symmetry but off-centre. The study explores the influence of supporting geometries on the conditions to initiate and propagate subsurface "radial" cracks, which are believed to be responsible for catastrophic failure of brittle-coating-based structures in certain applications, such as dental crowns. It is demonstrated that critical loads for initiation of radial cracks and the subsequent crack propagation are insensitive to complex geometry, so that simple monotonic indentation "axis and/or off-axis loading" with minimum geometrical complication "flat, simply curved" remains an appropriate route to study the evolution of radial cracks in practical brittle coating structures. (c) 2005 Elsevier Ltd. All rights reserved.