Abstract: The stability of sheet electron beams transporting in periodic magnet fields with natural focusing are studied using numerical calculation and PIC simulation. The focusing period affects the stability of beams greatly. It is shown that high voltage beams require Wiggler rather than PCM fields for periodic focusing and the periodic magnet structures with small period require precise machining. It is assumed that the cross-sections of the channel and the beam have attainable shapes and the periodic focusing structures are semi-infinite. The results presented in this paper are helpful for guiding the practical engineering design.