The compressive resistance of truncated nanocone lattices produced by lithography and etching steps on Si or Ge wafers to get superhydrophobic and antireflective light transmitting windows, as well as the protection efficiency of alumina or diamond coatings are investigated by numerical simulations of elastic buckling, and nano-compression tests. The latter reveal the limits of an elastic analysis, since the stress at the top of the cones is high enough to trigger plastic flow, or phase changes. Ge nano-cones exhibit a large ductility in compression, and even seem to creep at room temperature. Thin alumina or diamond coatings are however shown to provide an effective protection against both buckling and plastic flow. Surface patterning is shown to induce stress concentrations at the foot of the cones, which reduces the fracture resistance of the substrate in biaxial bending.