  A long cylindrical cavity through a soft solid forms a soft microfluidic
channel, or models a vascular capillary. We observe experimentally that, when
such a channel bears a pressurized fluid, it first dilates homogeneously, but
then becomes unstable to a peristaltic elastic instability. We combine theory
and numerics to fully characterize the instability in a channel through a bulk
neo-Hookean solid, showing that instability occurs supercritically with
wavelength $2\pi/k=12.278....a$ when the pressure exceeds $2.052....\mu$. In
finite solids, the threshold pressure is reduced, and peristalsis is followed
by a second instability which shears the peristaltic shape breaking
axisymmetry. These instabilities shows that, counterintuitively, if a pipe runs
through a bulk solid, the bulk solid can be destabilizing rather than
stabilizing at high pressures. They also offers a route to fabricate
periodically undulating channels, producing waveguides with photonic/phononic
stop bands.
