  Shock breakout is the first electromagnetic signal from supernovae (SNe),
which contains important information on the explosion energy and the size and
chemical composition of the progenitor star. This paper presents the first
two-dimensional (2D) multi-wavelength radiation hydrodynamics simulations of SN
1987A shock breakout by using the $\texttt{CASTRO}$ code with the opacity
table, $\texttt{OPAL}$, considering eight photon groups from infrared to X-ray.
To investigate the impact of the pre-supernova environment of SN 1987A, we
consider three possible circumstellar medium (CSM) environments: a steady wind,
an eruptive mass loss, and the existence of a companion star. In sum, the
resulting breakout light curve has an hour duration and its peak luminosity of
$\sim 6\times 10^{46}\,\rm{erg\,s^{-1}}$ then following a decay rate of $\sim
3.5\,\rm{mag\,hour^{-1}}$ in X-ray. The dominant band transits to UV around 3
hours after the initial breakout, and its luminosity has a decay rate of $\sim
1.5\,\rm{mag\,hour^{-1}}$ that agrees well with the observed shock breakout
tail. The detailed features of breakout emission are sensitive to the
pre-explosion environment. Furthermore, our 2D simulations demonstrate the
importance of multidimensional mixing and its impacts on shock dynamics and
radiation emission. The mixing emerging from the shock breakout may lead to a
global asymmetry of SN ejecta and affect its later supernova remnant formation.
