  We present cosmological simulations which closely mimic the real Universe
within 100Mpc of the Local Group. The simulations, called Constrained
Simulations, reproduce the large-scale density field with major nearby
structures, including the Local Group, the Coma and Virgo clusters, the Great
Attractor, the Perseus-Pices, and the Local Supercluster, in approximately
correct locations. The MARK III survey of peculiar velocities of the observed
structures inside 80Mpc/h sphere is used to constrain the initial conditions.
Fourier modes on scales larger then 5Mpc/h are dominated by the constraints,
while small scale waves are random. The main aim of this paper is the structure
of the Local Supercluster (LSC; 30Mpc/h around the Virgo cluster) and the Local
Group environment. We find that at the current epoch most of the mass
(7.5e14Msun/h) of the LSC is located in a filament roughly centered on the
Virgo cluster and extending over 40Mpc/h. The simulated Local Group (LG) is
located in an adjacent smaller filament, which is not a part of the main body
of the LSC, and has a peculiar velocity of 250kms toward the Virgo cluster. The
peculiar velocity field in the LSC region is complicated and is drastically
different from the field assumed in the Virgocentric infall models. The
peculiar velocity flow in the vicinity of the LG in the simulation is ``cold'':
the peculiar line-of-sight velocity dispersion within 7Mpc/h of the LG is less
than 60km/s, comparable to the observed velocity dispersion of nearby galaxies.
