The remarkable optoelectronic and especially photovoltaic performance of hybrid organic–inorganic perovskite (HOIP) materials drives efforts to connect materials properties to this performance. From nano-indentation experiments on solution-grown single crystals we obtain elastic modulus and nano-hardness values of APbX3 (A = Cs, CH3NH3; X = I, Br). The Young's moduli are ~14, 19.5, and 16 GPa, for CH3NH3PbI3, CH3NH3PbBr3, and CsPbBr3, respectively, lending credence to theoretically calculated values. We discuss the possible relevance of our results to suggested “self-healing”, ion diffusion, and ease of manufacturing. Using our results, together with literature data on elastic moduli, we classified HOIPs amongst the relevant material groups, based on their elastomechanical properties.