Creations of light anti-nuclei (anti-deuterium, anti-tritium, antiHe3 and anti-He4) are observed by collaborations at the LHC and RHIC accelerators. Some cosmic ray experiments are aimed to find the anti-nuclei in cosmic rays. To support the experimental studies of the anti-nuclei a Monte Carlo simulation of anti-nuclei interactions with matter is implemented in the Geant4 toolkit. The implementation combines practically all known theoretical approaches to the problem of antinucleon-nucleon interactions.Keywords anti-nucleus · anti-proton · cross sections · annihilation · quark-gluon string model