A model is introduced to describe the transverse electromagnetic propagation of power in high‐voltage vacuum transmission lines in the presence of a resistive cathode plasma. The model consists of the transmission line equations complemented with a one‐dimensional model for calculating local shunting currents. These equations are self‐consistently solved in the presence of a cathode plasma expanding against the magnetic field. The plasma motion, considered to start at a given point when the local electric field reaches the selected threshold value of 0.3 MV/cm, is described by using one‐dimensional magnetohydrodynamic equations in which the plasma properties at each position along the length of the line are assumed to depend only on the cross cathode‐anode direction. Magnetic diffusion is taken into account in the plasma as well as in the metal cathode. The model is applied to a system for which experimental results are available: a 2‐m vacuum coaxial line of Al walls, driven by a voltage pulse of 130‐ns duration and 0.5‐MV peak, of 6.2‐cm radius and 0.5‐cm gap terminated by an 18‐nH inductive load. Several calculations with different initial temperatures and densities were performed assuming an Al plasma in local thermal equilibrium of variable degree of ionizationz¯.For the highest initial values of temperature and areal density used,T= 5 eV, &mgr; = 8.7×10−7g/cm2, the average plasma front velocity was 2.4×106cm/s. For this case the plasma is found to carry about 50% of the line current once its size is of the order of 1 mm, and it is almost stopped by the magnetic field, which reaches 25 kG at 130 ns. The calculated values of the line and shunting currents at different positions along the coax are compared with the experimental values. It is shown that the line currents are higher than if no plasma were present and lower than if it were a moving perfect conductor. For lower temperatures and densities, the average plasma front velocities are lower, of the order of 2×106cm/s. To assess the possible influence of anomalous effects anadhocmodel for resistivity, in which it is equal to the inverse of the electron plasma frequency, is introduced. ForT= 5 eV and &mgr; = 8.7×10−7g/cm2, thisadhocmodel which clearly underestimates the influence of the magnetic field in slowing down the plasma, gives average plasma front velocities of 3.5×106cm/s. On the basis of these calculations, it is concluded that for the type of experimental setup under consideration, no plasma closure should be observed, even when active loads are used, within the framework of the physical phenomena considered here. The importance of considering magnetic diffusion and joule heating in the motion of the cathode plasma as it influences the electrical properties of vacuum lines is demonstrated.