[en] Statistical Monte Carlo simulation of cascade showers generated by high energy particles in extended gaseous and condensed media - in atmosphere, in radiation protection materials, in fissionable matters etc., is discussed. The parameters of nuclear interactions in which shower particles are produced, scattered and absorbed, are also calculated using the Monte Carlo method on the basis of experimental data on elementary particle interactions. In the region of very high energies, where the data are insufficient, the information on elementary particle interactions could be calculated using Monte Carlo method applied to the ''deep'' processes of production, propagation and decay of quark-gluon strings. The nuclear-physical processes which calculation is connected with the simulation of particle showers in media, are discussed