The VULCAN CFD code integrated with a reduced chemical kinetic mechanism was applied to simulate cavity-stabilized ethylene-air flames and to predict flame stability limits in supersonic flows based on an experimental study. A 15-step reduced kinetic mechanism for ethylene was systematically developed through skeletal reduction with a directed relation graph and time scale reduction based on quasi-steady state assumptions. The accuracy of the reduced kinetic mechanism and its implementation in the VULCAN code were demonstrated in an auto-ignition problem with a range of parameters. 3D simulations were then carried out for cavity-stabilized flames at different fuel flowrates and turbulent Schmidt numbers. For comparison with the performance of the present reduced mechanism, a 3- and a 10-step global kinetic model were applied to simulate the same cavity combustor, and the results show that the 15-step reduced model predicts experimental results much better than the 3- and 10-step models. The importance of including accurate chemical kinetics in CFD simulations is therefore demonstrated.