  Combining a classical force field, a tight-binding model, and
first-principles calculations, we have studied structural, electronic, and
optical properties of double-walled carbon nanotube (DWNT) bundles under
hydrostatic pressure. We find that the outer tube acts as a protection shield
for the inner tube and the inner tube increases the structure stability and the
ability to resist the pressure of the outer tube. Moreover, the collapsed
structures of the double-walled carbon nanotube bundle called ``parallel'' and
``in-between'' are more stable than the one called ``herringbone''. The
structural phase transition induces a pseudogap along symmetry line
\textit{$\Gamma $X}. Furthermore, the optical properties change greatly after
the collapse and a strong anisotropy appears in the collapsed structure. This
provides an efficient experimental way to detect structural phase transitions
in DWNT bundles.
