Extinction limits and the lean flammability limit of non-adiabatic stretched premixed methane–air flames are investigated numerically with detailed chemistry and two different Planck mean absorption coefficient models. Attention is paid to the combined effect of radiative heat loss and stretch at low stretch rate. It is found that for a mixture at an equivalence ratio lower than the standard lean flammability limit, a moderate stretch can strengthen the combustion and allow burning. The flame is extinguished at a high stretch rate due to stretch and is quenched at a low stretch rate due to radiation loss. A O-shaped curve of flame temperature versus stretch rate with two distinct extinction limits, a radiation extinction limit and a stretch extinction limit respectively on the left- and right-hand sides, is obtained. A C-shaped curve showing the flammability limit of the stretched methane–air flame is obtained by plotting these two extinction limits in the mixture strength coordinate. A good agreement is shown on comparing the predicted results with the experimental data. For equivalence ratio larger than a critical value, it is found that the O-shaped temperature curve opens up in the middle of the stable branch, so that the stable branch divides into two stable flame branches; a weak flame branch and a normal flame branch. The weak flame can survive between the radiation extinction limit and the opening point (jump limit) while the normal flame branch can survive from its stretch extinction limit to zero stretch rate. Finally, a G-shaped curve showing both extinction limits and jump limits of stretched methane–air flames is presented. It is found that the critical equivalence ratio for opening up corresponds to the standard flammability limit measured in microgravity. Furthermore, the results show that the flammability limit (inferior limit) of the stretched methane–air flame is lower than the standard flammability limit because flames are strengthened by a moderate stretch at Lewis number less than unity.