As a method of non-traditional machining, EDM plays an important role in advanced manufacturing technology. The EDM process involves multi-physics coupling effects such as electromagnetics, thermal and fluid. It has the characteristics of instantaneity, randomness and complexity, which brings difficulties to the study of discharge process. In this paper, a multi-physics coupling model of the EDM discharge process is established based on magnetohydrodynamics, the discharge process is simulated transiently. Results show that the plasma channel is formed within 0.1μs, the highest current density and temperature are in the centre of the plasma channel, and gradually decrease along the radial direction with the increase of the radius, and there is little change along the axial direction; The electric field intensity between tools gradually stabilizes after the plasma channel is formed; The velocity of dielectric between tools takes the centre of the plasma channel as the axis of symmetry, in the form of a symmetrical vortex, with the direction from tool to workpiece, and the maximum velocity is at the centre of the tools.