An analytical study was conducted to supplement recent high-pressure shock tube measurements of CH4/O-2, ignition at elevated pressures (40-260 atm), low dilution levels (fuel plus oxidizer greater than or equal to 30%), intermediate temperatures (1040-1500 K), and equivalence ratios as high as 6. A 38-species, 190-reaction kinetics model, based on the Gas Research Institute＇s GRI-Mech 1.2 mechanism, was developed using additional reactions that are important in methane oxidation at lower temperatures. The detailed-model calculations agree well with the measured ignition delay times and reproduce the accelerated ignition trends seen in the data at higher pressures and lower temperatures. Although the expanded mechanism provides a large improvement relative to the original model over most of the conditions of this study further improvement is still required at the highest CH4 concentrations and lowest temperatures. Sensitivity and species flux analyses were used to identify the primary reactions and kinetics pathways for the conditions studied. In general, reactions involving HO2, CH3O2, and H2O2 have increased importance at the conditions of this work relative to previous studies at lower pressures and higher temperatures. At a temperature of 1400 K and pressure of 100 atm, the primary ignition promoters are CH3 + O-2 = O + CH3O and HO2 + CH3 = OH + CH3O. Methyl recombination to ethane is a primary termination reaction and is the major sink for CH3 radicals. At 1100 K, 100 atm, the dominant chain-branching reactions become CH3O2 + CH3 = CH3O + CH3O and H2O2 + M = OH + OH + M. These two reactions enhance the formation of H and OH radicals, explaining, the accelerated ignition delay time characteristics at lower temperatures (19.0 kcal/mol activation energy at 1100 K versus 32.7 kcal/mol at 1400 K). A literature review indicated few measurements exist for many of the most influential rate coefficients, suggesting the need for further study in this area. This paper represents a first step toward understanding the kinetics of CH4 ignition and oxidation at the extreme conditions of the shock tube experiments.