This study has been mainly motivated to numerically model the transcritical mixing and reacting flow processes encountered in the liquid propellant rocket engines. In the present approach, turbulence is represented by the extended k-3 turbulence model. To account for the real fluid effects, the propellant mixture properties are calculated by using SRK (Souve-Redlich-Kwong) equation of state model. In order to realistically represent the turbulence-chemistry interaction in the turbulent non-premixed flames, the flamelet approach based on the real fluid flamelet library has been adopted. Based on numerical results, the detailed discussions are made for the real fluid effects and the precise structure of the transcritical cryogenic liquid nitrogen jet and gaseous hydrogen/liquid oxygen coaxial jet flame.