  Much recent attention has been devoted towards unravelling the microscopic
optoelectronic properties of hybrid organic-inorganic perovskites (HOP). Here
we investigate by coherent inelastic neutron scattering spectroscopy and
Brillouin light scattering, low frequency acoustic phonons in four different
hybrid perovskite single crystals: MAPbBr$_3$, FAPbBr$_3$, MAPbI$_3$ and
$\alpha$-FAPbI$_3$ (MA: methylammonium, FA: formamidinium). We report a
complete set of elastic constants caracterized by a very soft shear modulus
C$_{44}$. Further, a tendency towards an incipient ferroelastic transition is
observed in FAPbBr$_3$. 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 $\alpha$-FAPbI$_3$.
