A programmable resistance memory device includes a semiconductor substrate, at least one cell array, in which memory cells are arranged formed above the semiconductor substrate. Each of the memory cells has a stack structure of a programmable resistance element and an access element, the programmable resistance element storing a high resistance state or a low resistance state determined due to the polarity of voltage application in a non-volatile manner. The access element has such a resistance value in an off-state in a certain voltage range that is ten time or more as high as that in a select state. A read/write circuit is formed on a semiconductor substrate as underlying the cell array for data reading and data writing in communication with the cell array.