A new concept of assembling layer-like structures from identical convex elements interlocked by virtue of their geometry and spatial arrangement was developed recently. In particular, identical cubes can be arranged in this type of assembly, such that none of them can be removed from the structure. This is achieved through the kinematic constraint imposed by the neighbouring elements, provided that a constraining frame substitutes for neighbours along the periphery of the assembly. We report experimental results and the results of numerical simulation showing that such assemblies exhibit a highly non-linear response to out-of-plane point loads (indentation), in particular a pronounced loading/unloading hysteresis, post-peak softening, a negative stiffness in the stage of unloading and localisation of irreversible rotations. The results of the simulations confirm that the observed unusual mechanical response is an intrinsic, material-independent property of such assemblies. (C) 2008 Elsevier Ltd. All rights reserved.