Abstract: The focusing properties of the electric field distribution in a linear inductionaccelerator gap are identical to those of a bipotential electrostatic lens if theparticle gap-transit time is small compared with the time variation of the inducedelectric field. Bipotential lenses are studied systematically only in the nonreletivis-tic case. In this paper we present the results of a theoretical study of the focusingproperties of a symmetrical two-cylinder lens with identical radii and negligibleseparation for relativistic electron beams. Analytical formulas derived by usingthe thin-lens approximation are compared with the results of numerical integrationof the relativistic paraxial ray equation and found to be sufficiently accurate for-practical applications.