This work presents a study of non-premixed flames at supercritical-pressure conditions. Emphasis is placed on flame stability in liquid rocket engines fueled with liquid oxygen and gaseous hydrogen. The flame structure sensitivity to strain, pressure, temperature and real-fluid effects was investigated in detailed opposed-jet flames calculations. It is shown that the flame is very robust to strain, that the flamelet assumption is valid for the conditions of interest, and that real-fluid phenomena can have a significant impact on flame topology. At high-pressure supercritical conditions, small pressure or temperature variations can induce strong changes of thermodynamic properties across the flame. A substantial finding was also that the presence of water from combustion significantly increases the critical pressure of the mixture, but this does not lead to a saturated state where two-phase flow may be observed. The present study then shows that a single-phase real-fluid approach is relevant for supercritical hydrogen-oxygen combustion. Resultant observations are used to develop a flamelet model framework that combines detailed real-fluid thermodynamics with a tabulated chemistry approach. The governing equation for energy contains a compressible source term that models the flame. Through this approach, the solver is capable of capturing compressibility and strain-rate effects. Good agreements have been obtained with respect to detailed computations. Heat release sensitivity to strain and pressure variations is also recovered. Consequently, this approach can be used to study combustion stability in actual burners. The approach preserves the density gradient in the high-shear region between the liquid-oxygen jet and product rich flame region. The latter is a key requirement to properly simulate dense-fluid jet destabilization and mixing in practical devices. (C) 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.