An experimental and modeling study of the autoignition of \(\hbox {CH}_{4}\) – \(\hbox {O}_{2}\) – \(\hbox {Ar}\) mixtures with 0.25–4.0% \(\hbox {CH}_{\textrm{4}}\) and 2.0% \(\hbox {O}_{\textrm{2}}\) was performed at reflected shock wave conditions of \(\sim \) 2 atm and \(\sim \) 1600–2300 K. The process was monitored by recording the absorption time profiles of \(\hbox {CH}_{\textrm{3}}\) and OH radicals at 216.6 nm and 306.772 nm, respectively. The ignition delay time was determined in two ways: as the times it takes to reach the peak \(\hbox {CH}_{\textrm{3}}\) concentration or one-half of the maximum OH concentration. Kinetic simulations were carried out using a number of reaction mechanisms, and the predictions were compared to the measurements. An analysis of the sensitivity of the ignition delay time to the rate constants of various elementary stages was conducted, and the main reactions controlling the ignition process were identified. It was demonstrated that uncertainties in experimental conditions, such as the initial temperature and pressure rise rate, produce an effect comparable with that stemming from uncertainties in the rate constants of the key reactions.