  We present a new three-dimensional Monte-Carlo code MUSIC (MUon SImulation
Code) for muon propagation through the rock. All processes of muon interaction
with matter with high energy loss (including the knock-on electron production)
are treated as stochastic processes. The angular deviation and lateral
displacement of muons due to multiple scattering, as well as bremsstrahlung,
pair production and inelastic scattering are taken into account. The code has
been applied to obtain the energy distribution and angular and lateral
deviations of single muons at different depths underground. The muon
multiplicity distributions obtained with MUSIC and CORSIKA (Extensive Air
Shower simulation code) are also presented. We discuss the systematic
uncertainties of the results due to different muon bremsstrahlung
cross-sections.
