  Ground-based atmospheric Cherenkov telescopes are proven to be effective
instruments for observations of very high energy (VHE) gamma-radiation from
celestial objects. For effective use of such technique one needs detailed Monte
Carlo simulations of gamma-ray- and proton/nuclei-induced air showers in Earth
atmosphere. Here we discuss in detail the algorithms used in the numerical code
ALTAI developed particularly for the simulations of Cherenkov light emission
from air showers of energy below 50 TeV. The specific scheme of sampling the
charged particle transport in the atmosphere allows the performance of very
fast and accurate simulations used for interpretation of the VHE gamma-ray
observations.
