Extinguishing limits of laminar ethylene/oxygen flames in both normal and inverse co-flow jet burner have been determined experimentally and computationally. An inert gas($N_2$, Ar, $CO_2$) was added into the oxidizer to find the critical concentration and the effectiveness of the agents on flame extinction. The experimental results showed that the physical aspect of inert gases was main mechanism for flame blow-out as same as cup burner test, but the flow effect should be considered to determine the extinction concentration. The numerical prediction was performed with modified WSR model and the result was in good agreement with the measurements. The experimental and numerical methods could be used for the assessment of various flame suppression agents such as minimum extinguishing concentration.