A 2D computational model, incorporating the Snowplow approximation in the mass balance, is used to simulate the acceleration of an annular current sheath along two coaxial electrodes, with the inner one having either cylindrical or conical shape. The circuit, mass and momentum equations are simultaneously solved in 2D (r, z) considering initial breakdown along the insulator surface, ideal gas mass accretion by the current sheath (snowplow model) and distributed inductance along a coaxial transmission line short-circuited by the current sheath. Plasma density and electron temperature in the current sheath are estimated using standard planar shock theory. Numerical integration of the model’s equations for a given electrode geometry yields the temporal evolution of the current sheath parameters during the axial acceleration phase. In order to see the effect of the inner electrode shape on sheath parameters (i.e. transit time, kinetic energy, total mass, shape, etc.) and/or circuit properties (i.e. circuit inductance, voltage and current evolution, etc.), the portion of the inner electrode beyond the insulator was given a conical shape. By changing the cone slant in a range between ±5°, it was found that the current driven on the plasma sheath varies nonlinearly with the angle. The divergent (positive angle) electrode gives the sheath the highest kinetic energy, being twice the value corresponding to that of the straight inner electrode case, and the transit time is reduced from 1.34 to 1.20 µs. The estimates of plasma density and electron temperature indicate that the achievable ion densities are on the order of 4x1022 m-3, which corresponds to 30 % ionization, and typical temperatures at the end of the rundown phase are on the order of 8 eV. These values are comparable with those measured in experimental devices. The development of this tool will enable us to benchmark its results against an experimental installation currently close to being operational, and a future follow-up paper will be devoted to the comparison between the prediction of the rundown phase behavior and experimental results utilizing conical electrodes.