Thin conducting foils focus charged particle beams through image charges induced on the foils. Such focusing has led to the suggestion that foils be used to transport intense, relativistic electron beams in high‐energy accelerators. This paper examines some of the limitations of foil focusing including sensitivity to the beam parameters, emittance growth from anharmonic focusing, and beam stability in multifoil transport. The analysis is based on a thin‐lens electrostatic treatment of paraxial beams.