We study the mechanical response under large elastic strains of pentamode layers confined between stiffening plates, and the potential use of such systems as novel seismic isolation and impact protection devices. We analyze pentamode materials that exhibit three soft deformation modes in the infinitesimal stretching regime that follow by the presence of perfectly hinged connections between the rods. The response of these metamaterials under large elastic strains is characterized by an elastic-stiffening effect in terms of the lateral force-displacement response, which increases in the presence of rigid connections and decreases by increasing the number of layers. Our results lead us to conclude that the analyzed pentamode metamaterials can ...