Abstract The new concept of rechargeable fluoride ion batteries (FIBs) could potentially be safer, cheaper and higher energy density than those of traditional batteries. However, due to the higher working temperature (~340 K) and the choice of electrolytes and electrodes with excellent electrochemical performance, FIBs are not utilized in daily life yet. In our work, we have systematically investigated several critical parameters of M2CH2 (M = Ti or V) MXenes to assess their performances as cathode materials for rechargeable FIBs, including energetic stability and thermal dynamic stability, electronic property, strain-driven ionic mobility, average open circuit voltage and theoretical specific capacity. Specifically, the ground state structures of M2CH2 are firstly confirmed and then F ion adsorption behavior on the substrate is investigated. Sequentially, F− microscopic diffusion path and migration barrier are identified with and without driven by strain. It reveals that Ti2CH2 displays a lower F− diffusion energy barrier than that of V2CH2 monolayer in a large strain span. Besides, an appropriate control of compression strain could effectively increase the F− mobility due to the change of surface state on Ti2CH2. Importantly, the obtained results show that the F− intercalation into Ti2CH2 exhibits a larger storage capacity (488 mA h g−1) and higher open circuit voltage (4.62 V) than these into V2CH2 monolayer. Moreover, ab initio molecular dynamics (AIMD) calculations prove F2Ti2CH2 is thermo-dynamically stable at 500 K, while, HF compound emerges on F2V2CH2 monolayer at 300 K, implying that Ti2CH2 cathode is possible to work at harshest environment. A combination of these key parameters, we demonstrate that Ti2CH2 monolayer has potential to be a flexible and strain-controllable cathode material for rechargeable FIBs. We hope our detailed investigations could serve as a motivation and provide valuable insights for future experiments to design flexible and dynamically stable cathode materials of high-performance FIBs.