  An extensive 3-dimensional Monte Carlo calculation of the atmospheric
neutrino flux is in progress with the FLUKA Monte Carlo code. The results are
compared to those obtained under the 1-dimensional approximation, where
secondary particles and decay products are assumed to be collinear to the
primary cosmic ray, as usually done in most of the already existing flux
calculations. It is shown that the collinear approximation gives rise to a
wrong angular distribution of neutrinos, essentially in the Sub-GeV region.
However, the angular smearing introduced by the experimental inability of
detecting recoils in neutrino interactions with nuclei is large enough to wash
out, in practice, most of the differences between 3-dimensional and
1-dimensional flux calculations. Therefore, the use of the collinear
approximation should have not introduced a significant bias in the
determination of the flavor oscillation parameters in current experiments.
