The rate of molecular dissociation behind strong shock waves is calculated with the assumption that dissociation can occur preferentially from the higher vibrational levels. An exponential probability of dissociation from the various vibrational levels is employed using an anharmonic oscillator model. Results for the dissociation of oxygen in an argon diluent are presented. Vibrational non‐equilibrium introduces aT−3temperature dependence into the oxygen dissociation rate constant in the range 4000°–8000°K. A dissociation lag‐time of the order of the extrapolated vibrational relax ation time is predicted immediately behind the shock front. The computed results are shown to be in agreement with available experimental results.