A semiconductor memory device (DRAM) includes a plurality of island regions, at least one cell transistor disposed on each island region and a cylindrical capacitor surrounding each island region. With such a structure, the capacity of the cell capacitor incorporated into a small space can be increased. Furthermore, a method of fabricating a semiconductor memory device includes a step of forming a groove having a necessary depth in a semiconductor substrate, a step of depositing a membrane having excellent covering characteristics in the groove, a step of etching by using an etching method having a strong anisotropy in the vertical direction while leaving the deposited membrane on a sidewall, and a step of etching the exposed portion of the semiconductor surface deeper in the groove and forming a capacity element and isolation region by using this deep trench.