Much recent attention has been devoted towards unraveling the microscopic optoelectronic properties of hybrid organic-inorganic perovskites. Here we investigate by coherent inelastic neutron scattering spectroscopy and Brillouin light scattering, low frequency acoustic phonons in four different hybrid perovskite single crystals: MAPbBr3, FAPbBr3, MAPbI3, and α-FAPbI3 (MA: methylammonium, FA: formamidinium). We report a complete set of elastic constants characterized by a very soft shear modulus C44. Further, a tendency towards an incipient ferroelastic transition is observed in FAPbBr3. We observe a systematic lower sound group velocity in the technologically important iodide-based compounds compared to the bromide-based ones. The findings suggest that low thermal conductivity and hot phonon bottleneck phenomena are expected to be enhanced by low elastic stiffness, particularly in the case of the ultrasoft α-FAPbI3.