  We have studied the hadronic interaction for the calculation of the
atmospheric neutrino flux by summarizing the accurately measured atmospheric
muon flux data and comparing with simulations. We find the atmospheric muon and
neutrino fluxes respond to errors in the $\pi$-production of the hadronic
interaction similarly, and compare the atmospheric muon flux calculated using
the HKKM04 code with experimental measurements. The $\mu^++\mu^-$ data show
good agreement in the 1$\sim$30 GeV/c range, but a large disagreement above 30
GeV/c. The the $\mu^+/\mu^-$ ratio shows sizable differences at lower and
higher momenta for opposite directions. As the disagreements are considered to
be due to assumptions in the hadronic interaction model, we try to improve it
phenomenologically based on the quark parton model. The improved interaction
model reproduces the observed muon flux data well. The calculation of the
atmospheric neutrino flux will be reported in the following paper
