The initiation of chemical reaction in cold-rolled Ni/Al multilayered composites by shock compression is investigated numerically. A simplified approach is adopted that exploits the disparity between the reaction and shock loading timescales. The impact of shock compression is modeled using CTH simulations that yield pressure, strain, and temperature distributions within the composites due to the shock propagation. The resulting temperature distribution is then used as initial condition to simulate the evolution of the subsequent shock-induced mixing and chemical reaction. To this end, a reduced reaction model is used that expresses the local atomic mixing and heat release rates in terms of an evolution equation for a dimensionless time scale reflecting the age of the mixed layer. The computations are used to assess the effect of bilayer thickness on the reaction, as well as the impact of shock velocity and orientation with respect to the layering. Computed results indicate that initiation and evolution of the reaction are substantially affected by both the shock velocity and the bilayer thickness. In particular, at low impact velocity, Ni/Al multilayered composites with thick bilayers react completely in 100 ms while at high impact velocity and thin bilayers, reaction time was less than 100 μs. Quantitative trends for the dependence of the reaction time on the shock velocity are also determined, for different bilayer thickness and shock orientation.