Abstract <p>The work is devoted to the mathematical modeling of the initiation of gas detonation in a channel with a profiled end wall. The two-dimensional geometry of the channel filled with a model hydrogen-oxygen mixture is considered. The mathematical model is based on the system of Euler equations supplemented by Arrhenius kinetics. Numerical experiments are carried out using triangular computational grids and the finite volume method. The formation of detonation waves occurs as a result of reflection of the incident plane shock wave with a Mach number of 2.45 from the end of the channel consisting of two elliptical fragments and sections of the flat wall. The distance between the elliptical sections varied widely to study the influence of this parameter on the processes of ignition of the mixture and formation of detonation waves. A nonlinear dependence of the detonation initiation time on this parameter was obtained. The nonlinear dependence is associated with different degrees of influence of factors affecting the intensity of the process of mixture combustion and the formation of detonation waves.</p>