The article presents the results of computer simulation of the propagation of the combustion wave of "self-propagating high-temperature synthesis (SHS)" process in an atomic layered structure. In each layer of the structure, nanosized blocks of two types alternate: a block of the first type is composed as a packet of unit cells of Ni atoms, and a block of the second type is composed of a packet of elementary cells of Al atoms. In each pair of layers adjacent to each other, sequences of alternating blocks of two types are shifted relative to each other by one block, so the full layered structure of the layers with alternating blocks in them is associated with a chessboard pattern. Computer simulation of SHS in such a structure was carried out using the LAMMPS software package taking into account parallel computations, which uses the molecular dynamics method and the interatomic interaction potential in the embedded atom" model (EAM). In addition to the LAMMPS package, the authors implemented program procedures for calculating the temperature and density profiles of the substance along the motion direction of the SHS combustion wave front, which made it possible to carry out temperature analysis of the SHS microkinetics (to estimate the velocity of the combustion wave front) and recognition of intermetallic phases in the reaction volume of the Ni-Al system when using the OVITO package.