We model interactions of protons and neutrons with energies from 1 to 1000 MeV with 241Am and 243Am nuclei. The calculations are performed with the Monte Carlo model for Accelerator Driven Systems (MCADS) which we developed based on the GEANT4 toolkit of version 9.4. This toolkit is widely used to simulate the propagation of particles in various materials which contain nuclei up to uranium. After several extensions we apply this toolkit also to proton- and neutron-induced reactions on Am. The fission and radiative neutron capture cross sections, neutron multiplicities and distributions of fission fragments were calculated for 241Am and 243Am and compared with experimental data. As demonstrated, the fission of americium by energetic protons with energies above 20 MeV can be well described by the Intra-Nuclear Cascade Liège (INCL) model combined with the fission-evaporation model ABLA. The calculated average numbers of fission neutrons and mass distributions of fission products agree well with the corresponding data. However, the proton-induced fission below 20 MeV is described less accurately. This is attributed to the limitations of the Intra-Nuclear Cascade model at low projectile energies.