In recent years, LOX-Methane propellant combination has attracted lot of attention because of its various advantages compared to typical LOX-Hydrogen rocket engines. ISRO is currently envisioning a 10T class methane engine to replace existing propulsion system in its launch vehicles. Transcritical methane experience large thermodynamic and transport property variations at pseudo-critical temperature (near-critical fluid) which can significantly influence flow field and heat transfer characteristics. It is prerequisite to understand combustion and heat transfer characteristics of methane for future engine development. A numerical study is initiated to analyze combustion and regenerative cooling performance of methane in rocket engine elements. Combustion behaviour and flame characteristics of LOX/Methane in typical shear co-axial injector have been investigated using non-adiabatic flamelet approach. Chemical kinetic mechanism (16 species, 41 reactions) is incorporated to accommodate nonequilibrium effects by flame straining due to transcritical injection. A separate assessment on thermo-fluidic behaviour of transcritical methane in rectangular regenerative channel subjected to asymmetric heating is also carried out. The conservation equations are suitably solved to determine heat transfer characteristics and associated stratification effect of transcritical methane flow through channel across the critical point. Thermo-physical properties of methane in transcritical to supercritical regime are modeled utilizing Soave-Redlich-Kwong (SRK) equation of state. The effect of aspect ratio of channels is investigated to understand their influence on heat transfer performance of regenerative cooling system in in Lox-Methane engine.