The propagation of a relativistic electron beam parallel to an array of parallel conductors, which provide charge and current neutralization of the beam, is investigated. Two geometries are studied: uniformly spaced planar foils or screens, and a matrix of parallel wires. The degree of charge and current neutralization and the resulting parallel and transverse fields are calculated for a uniform density pulse. The self‐consistent transverse equilibrium is derived for the planar foil geometry. The effects of injection perpendicular to a planar cathode are investigated. Particle simulations in planar and cylindrical geometries are presented to confirm the analysis and to study edge effects and containment of the beam within the array. Comparison to vacuum drift tube operation shows that such arrays of conductors may allow beam transport with currents far exceeding the vacuum limit.