  Recent observations have discovered a giant HI bridge that appears to connect
between the outer halo regions of M31 and M33. We propose that this HI bridge
can be formed as a result of the past interaction between M31 and M33 based on
test particle simulations with different orbits of M31 and M33 for the last ~ 9
Gyr. We show that strong tidal interaction between M31 and M33 about 4-8 Gyr
ago can strip HI gas from M33 to form HI streams around M31 which can be
observed as a HI bridge if they are projected onto the sky. We show that the
number fraction of models reproducing well the observed HI distribution of the
bridge is only ~0.01% (i.e., ~10 among ~10^5 models) and thus suggest that the
observed structure and kinematics of the HI bridge can give some constraints on
the past orbits of M31 and M33. We suggest that the observed outer HI warp in
M33 could be fossil evidence for the past M31-M33 interaction. We also suggest
that some of high velocity clouds (HVCs) recently found in M31 could be HI gas
originating from M33. We briefly discuss other possible scenarios for the
formation of the HI bridge.
