  We present a first-principles study of the energy and elastic properties of
solid helium at pressures below the range in which is energetically stable. We
find that the limit of mechanical stability in hcp 4He is $P_{s}$ = -33.82 bar,
which lies significantly below the spinodal pressure found in the liquid phase
(i.e., -9.6 bar). Furthermore, we show that the pressure variation of the
transverse and longitudinal sound velocities close to $P_{s}$ do not follow a
power law of the form $\propto \left( P - P_{s} \right)^{\gamma}$, in contrast
to what is observed on the fluid.
