The problem of direct initiation of detonation, where a powerful ignition source drives a blast wave into a gaseous combustible mixture to generate a Chapman–Jouguet (CJ) detonation, is investigated numerically by using a three-step chain-branching chemical kinetic model. The reaction scheme consists sequentially of a chain-initiation and a chain-branching step, followed by a temperature-independent chain termination. The three regimes of direct initiation i.e. subcritical, critical and supercritical, are numerically simulated for planar, cylindrical and spherical geometries using the present three-step chemical kinetic model. It is shown that the use of a more detailed reaction mechanism allows a well-defined value for the critical initiation energy to be determined. The numerical results demonstrate that detonation instability plays an important role in the initiation process. The effect of curvature for cylindrical and spherical geometries has been found to enhance the instability of the detonation wave and thus influence the initiation process. The results of these simulations are also used to provide further verification of some existing theories of direct initiation of detonation. It appears that these theories are satisfactory only for stable detonation waves and start to break down for highly unstable detonations because they are based on simple blast wave theory and do not include a parameter to model the detonation instability. This study suggests that a stability parameter, such as the ratio between the induction and reaction length, should be considered and a more complex chemistry should be included in future development of a more rigorous theory for direct initiation of detonation.