We present a new three-dimensional Monte-Carlo code MUSIC (MUon SImula
tion Code) for muon propagation through the rock. All processes of muo
n interaction with matter with high energy loss (including the knock-o
n electron production) are treated as stochastic processes. The angula
r deviation and lateral displacement of muons due to multiple scatteri
ng, as well as bremsstrahlung, pair production and inelastic scatterin
g are taken into account. The code has been applied to obtain the ener
gy distribution and angular and lateral deviations of single muons at
different depths underground. The muon multiplicity distributions obta
ined with MUSIC and CORSIKA (Extensive Air Shower simulation code) are
also presented. We discuss the systematic uncertainties of the result
s due to different muon bremsstrahlung cross-sections. (C) 1997 Elsevi
er Science B.V.