The simulation results of SHS process in a package of alternating nanoscale layers of the crystal lattices of Ti and Al atoms for two systems with various numbers of atoms and nonstoichiometric ratios are given. For simulation the LAMMPS package supporting parallel computations and the interatomic interaction potential in the “embedded atom” model (EAM) have been used. For two systems with various numbers of atoms and nonstoichiometric ratios the sets of temperature and density profiles along the layers of the structure at successive instants of time (up to 16 ns) have been obtained. For a system with 453974 atoms and a nonstoichiometric ratio of 1.23 the heterostructure emergence with an alternation of intermetallic phases when changing the SHS “ignition” temperature has been reproduced.