The blow-off limits of CH4/air flames in a mesoscale cavity-combustor under various pressures (P = 1.0 - 3.0 atm) are investigated numerically. The results show that the flame blow-off limit increases first and then decreases with an increasing pressure. Three typical pressures (P = 1, 2 and 3 atm) are selected to perform numerical analysis with a detailed reaction mechanism. The analysis demonstrates that the reaction intensity in the cavity is enhanced as the pressure is raised, which is beneficial for flame stability. On the other hand, the flame front is prolonged at a higher pressure. This leads to more intense stretching effect, which is detrimental for flame stability. Therefore, the flame blow-off limit depends on the competition between the positive and negative sides. When the pressure is increased from 1 atm to 2 atm, the enhancement of anchoring ability in the cavity overwhelms the augmentation of stretching effect, which leads to an increase in flame blow-off limit. However, as the pressure is further raised from 2 atm to 3 atm, the stretching effect becomes the dominated side, which results in a decrease in flame blow-off limit. In summary, these complicated interactions determine that the flame blow-off limit is a non-monotonic function of the pressure. (C) 2015 Elsevier Ltd. All rights -reserved.