  We implement molecular dynamics simulations in canonical ensemble to study
the effect of confinement on a $2d$ crystal of point particles interacting with
an inverse power law potential proportional to $r^{-12}$ in a narrow channel.
This system can describe colloidal particles at the air-water interface. It is
shown that the system characteristics depend sensitively on the boundary
conditions at the two {\it walls} providing the confinement. The walls exert
perpendicular forces on their adjacent particles. The potential between walls
and particles varies as the inverse power of ten. Structural quantities such as
density profile, structure factor and orientational order parameter are
computed. It is shown that orientational order persists near the walls even at
temperatures where the system in the bulk is in fluid state. The dependence of
elastic constants, stress tensor elements, shear and bulk modulii on density as
well as the channel width is discussed. Moreover, the effect of channel
incommensurability with the triangular lattice structure is discussed. It is
shown that incommensurability notably affects the system properties. We compare
our findings to those obtained by Monte Carlo simulations and also to the case
with the periodic boundary condition along the channel width. .
