The resonant tunneling phenomena in double-barrier structures have been studied both theoretically and experimentally by many researchers in these twenty years /1 to 7 1 . However, few theoretical studies have been made for the quadruple-barrier structure / 8 / . Especially, it seems that a study of the resonant tunneling for the symmetrical quadruple-barrier structure has not been carried out yet, though an interesting and useful feature for the resonant tunneling may be veiled. Actually, some interesting feature has been found in this structure. In this note, the analytical expressions for the transmission coefficient and the resonance condition are derived for the first time. It is believed that they are useful for evaluating the energy variation of the transmission coefficient and estimating the resonance energies in the symmetrical rectangular quadruple-barrier structure, and will provide an important foundation for device fabrication, which will not be obtained in the equivalent quadruple-barrier structure or in the double-barrier structure.The model potential to be studied is a symmetrical one-dimensional rectangular quadruple-barrier structure as depicted in Fig . . . , and x8). The energy origin is taken at the conaucnon Dana eage of the region 1 material. It is assumed that an electron with energy E is incident from the left and transmits to the right along the x-direction. The electron mass is assumed to be constant m* over the entire region of the structure. By matching the wave functions and their first derivatives at the boundary we can derive the transmission coefficient T4S for 0 < E < Vo after a straightforward algebra: