Abstract: Modular multilevel converter (MMC) is the main topology for the voltage source converter-based high voltage direct current (VSC-HVDC) project. The current through-flow capability of the semiconductor devices, especially that of the IGBTs of the MMC, is weak and the safety margin is small in high-voltage VSC-HVDC projects with large capacity. So it is decisive to calculate the steady-state current stress of the semiconductor devices accurately for the device selection, the converter loss calculation, the design of the valve cooling system, the valve operation state estimation and so on. Also, the supporting capacitor is the key component of the submodule, and its current is the key parameter to be considered when being developed. In this paper, the accurate analytical expression of the average value of the current, and the root-mean-square value of the current of the components in sub-modules are deduced, based on the current through-flow conditions and the average switching function model. Furthermore, the current stresses of the four devices are compared and their characteristics are analyzed when the MMC is in the converter and the inverter states. With the comparison of the analytical calculation results and the electromagnetic simulation results of the steady state current stress of the devices, the accuracy of the proposed analytical method is validated. Finally, the characteristics of the current stress distribution of the components are revealed based on the analytical calculation and simulation analysis.