  We present the results of a numerical simulation of propagation of cosmic
rays with energy above $10^{15}$ eV in a complex magnetic field, made in
general of a large scale component and a turbulent component. Several
configurations are investigated that may represent specific aspects of a
realistic magnetic field of the Galaxy, though the main purpose of this
investigation is not to achieve a realistic description of the propagation in
the Galaxy, but rather to assess the role of several effects that define the
complex problem of propagation. Our simulations of Cosmic Rays in the Galaxy
will be presented in Paper II. We identified several effects that are difficult
to interpret in a purely diffusive approach and that play a crucial role in the
propagation of cosmic rays in the complex magnetic field of the Galaxy. We
discuss at length the problem of the extrapolation of our results to much lower
energies where data are available on the confinement time of cosmic rays in the
Galaxy. The confinement time and its dependence on particles' rigidity are
crucial ingredients for 1) relating the source spectrum to the observed cosmic
ray spectrum; 2) quantifying the production of light elements by spallation; 3)
predicting the anisotropy as a function of energy.
