The application of the laminar flamelet concept to turbulent flame modeling requires a detailed understanding of stretched laminar flames. In this study, we used numerical methods, including arc-length continuation, to simulate the extinction characteristics of counterflow premixed fuel-lean, methane air flames. Attention was primarily paid to the effect of radiative heat loss on the extinction characteristics of these flames. The results show that at medium to low values of the stretch rate, the radiative heat loss has a particularly strong impact on the counterflow premixed fuel-lean, methane- air flames. It was also found that, in addition to the stretch extinction limit at a high stretch rate, there exits a radiation extinction limit at a low stretch rate. Furthermore, the relationship between these two extinction limits and the equivalence ratio is obtained.