The self-propagating high-temperature reaction in nickel-aluminum powder mixtures has been investigated by computer simulated experiments using a monodimensional model. The model describes the overall reaction mechanism considering several elemental steps such as melting of the reactant Al, diffusion-controlled dissolution of solid nickel into the molten pool, (possible) melting of the Ni reactant, precipitation and melting of the compound, and precipitation of the eutectic mixture of Al + AlNi. Melting of pure aluminum and nickel and eutectic crystallization are considered in terms of thermal balance only, whereas an explicit diffusion controlled kinetic for the dissolution of nickel in molten aluminum was accounted for. The results show that the reaction propagates under almost steady conditions with constant wave velocity and peak temperature, close to experimentally reported values, when suitable values for the thermal conductivity of the green compact were set.