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Radial oscillations of hollow, relativistic electron beams have been observed on Sandia’s RADLAC I, a multistage high‐current linear induction accelerator. These oscillations, which arise because the presence of the accelerating gaps prevents radial force balance, can be responsible for poor beam quality and low current‐transport efficiency. The method of magnetic field shaping to suppress oscillations is investigated. Two analytical models are formulated to derive nonuniform fields necessary to maintain force balance in a single‐gap geometry. Particle code simulations have been made to test beam propagation in contoured fields. Field shaping does suppress oscillations and is not sensitive to fluctuations in beam and gap parameters.