The stable characteristics of the DC fault are significant for the design and programming of the DC system, the configuration of the protection system, as well as the selection of the primary equipments. As for flexible DC system based on modular multilevel converter (MMC), the influence of the arm reactors on the commutation overlap during the uncontrolled rectification stage of the DC fault is addressed. This paper analyses the possible commutation overlapping angle ranges and the corresponding fault conditions. For different commutation overlapping angle ranges, the arm conducting working conditions are discussed, and then the calculation methods of the DC current, DC voltage, arm current and AC current during the stable state of the DC fault are proposed. Finally, the MMC-HVDC system model is built on the PSCAD/EMTDC platform. Simulation tests with different fault distances are carried out to verify the accuracy of the theoretical calculation.