Abstract: The development of the post-arc sheath of the vacuum circuit breaker is studied, and the arc plasma hydrodynamics equation is introduced to solve the drift-diffusion equation of electron, ion density and average electron energy and the Poisson equation of the coupled electric field. And the post arc sheath development time and cathode field intensity are analyzed from 1.0 to 20.0 km short-line fault breaking of the vacuum circuit breaker.The simulation results show that the shorter the sheath development time, the smaller RRRV, which is more conducive to successful breaking. In case of short-range fault, the sheath develops for a long time, and the electric field intensity of the post arc cathode is large, which is not conducive to post arc dielectric recovery. Under 3.0 km shortline fault breaking condition, the post arc cathode electric field intensity reaches the maximum. However, under 20.0 km short-line fault breaking condition, the maximum electric field intensity of the post arc cathode is reduced by 70.5%, the sheath development time is reduced by 34.5%, the probability of breakdown decreases, and the success rate of breaking increases.