This article reviews the state-of-the -art of mechanical material properties and measurement methods of nanostructures obtained by two nanoscale additive manufacturing methods: gas-assisted focused electron and focused ion beam-induced deposition using volatile organic and organometallic precursors. Gas-assisted focused electron and ion beam-induced deposition-based additive manufacturing technologies enable the direct-write fabrication of complex 3D nanostructures with feature dimensions below 50 nm, pore-free and nanometer-smooth high-fidelity surfaces, and an increasing flexibility in choice of materials via novel precursors. We discuss the principles, possibilities, and literature proven examples related to the mechanical properties of such 3D nanoobjects. Most materials fabricated via these approaches reveal a metal matrix composition with metallic nanograins embedded in a carbonaceous matrix. By that, specific material functionalities, such as magnetic, electrical, or optical can be largely independently tuned with respect to mechanical properties governed mostly by the matrix. The carbonaceous matrix can be precisely tuned via electron and/or ion beam irradiation with respect to the carbon network, carbon hybridization, and volatile element content and thus take mechanical properties ranging from polymeric-like over amorphous-like toward diamond-like behavior. Such metal matrix nanostructures open up entirely new applications, which exploit their full potential in combination with the unique 3D additive manufacturing capabilities at the nanoscale.