The primary objectives of this work are to implement ”realistic” chemical kinetics in large scale numerical simulations of methane flames, and to assess the structure of turbulent jet flames via such simulations. The methane flames, and to assess the structure of turbulent jet flames via such simulation. The oxidation mechanism is taken into account by the global 1-step model of Bhui-Pham (1992), the 4-step reduced mechanism developed by Seshadri and Peters(1988) and by Bilger et al. (1990a), and the skeletal 25-step mechanism of Smooke and Giovangigli(1990). Simulations are conducted of CH₄-air combustion in a homogeneous turbulent flow in which the hydrodynamic field is simulated via the linear eddy (LEM) of Kerstein(1988),. The composition structure of flames exhibits the difference between the 1-step and the reduced mechanisms. Direct numerical simulation (DNS) of a planar methane jet diffusion flame is conducted via the 1-step model to study the statistic of the near-field flame structure and to analyze the dynamics of the flame-vortex interactions. Some of the features captured by these simulations are shown to be in accord with experimental measurements. Large eddy simulation(LES) of unsteady methane jet flame is conducted via the “filter mass density function” (FMDE) of Jaberi et al. (1998). The FMDF represents the single point probability function (PDF) of the mass weighted subgrid (SGS) scalar quantities, ,and therefore accounts foe the effects o