  Knowledge of atmospheric muon flux intensity at large depths is extremely
important for neutrino telescopes located deep under ground, water or ice. One
of the methods to transform muon sea-level spectrum into depth one is to apply
Monte Carlo technique which directly takes into account stochastical nature of
energy loss. In order to decrease computation time down to acceptable level one
has to use simplifications resulting in systematic errors which in some cases
may distort result essentially. Here in this paper we present our analysis for
dependence of computed depth muon flux upon the most important parameters of
muon transport Monte Carlo algorithm which was done with the MUM (MUons+Medium)
code. Contribution of different simplifications to the resulting error is
considered, ranked and compared with uncertainties which come from
parametrization accuracy both for sea-level muon spectrum and for muon cross
sections.
