An explicit, time accurate, predictor-corrector scheme, similar to MacCormack’s has been used to simulate unsteady non-equilibrium, laminar chemically reacting diffusion-reaction generated flows. A zonal approach, along with non-structured boundaries, allows computation of internal and external flow with the same computer code. Results for equilibrium flows generated by dissociating, vibrationally relaxing nitrogen in a rectangular chamber are presented. The unsteady flows were generated strictly by.the chemical reactions and concentration gradients.