A recent investigation of flash-back of flames on slit and cylindrical burners showed that there is a systematic difference of about 10% between flash-back gradients of flames on slit and cylindrical burners with a burner diameter/width of 3.8 mm. In addition, the critical gradients become almost equal for burners with a diameter/width larger than about 6 mm. In this paper the effect of the burner wall curvature on the behaviour of, for example, the temperature field and the stand-off distance is analysed. The analysis shows that the burner wall curvature has an effect on the quenching layer thickness near the burner wall for burners smaller than about 6 mm. When the decrease of the cylindrical stand-off distance with increasing burner size is used to calculate the critical flash-back gradient based on a linear velocity profile for the cylindrical burners, the critical gradients for cylindrical and slit burners become almost the same for burners larger than about 5 mm. The analysis shows that the differences between flames on cylindrical and slit burners near the flash-back limit are mainly caused by differences in conductive heat transfer towards the burner wall, induced by burner wall curvature.