The present paper studies failure processes of detonation waves propagating in an expanding channel by conducting numerical simulations. A computational procedure, which combines the random choice method with a chemical kinetics simulation code and a step for the effects of the cross-sectional area of the channel, is applied to simulate gasdynamic and chemical phenomena of one-dimensional detonation waves moving through an expanding channel filled with hydrogen and oxygen diluted in an argon mixture. Also, two-dimensional simulations are carried out and compared with the one-dimensional results. It is shown that the present one-dimensional simulations calculate averaged flowfields of the two-dimensional results over the cross section of the channel.