A method for manufacturing an electrically programmable non-volatile memory cell comprises forming a first electrode on a substrate, forming an inter-electrode layer of material on the first electrode having a property which is characterized by progressive change in response to stress, and forming a second electrode over the inter-electrode layer of material. The inter-electrode layer comprises a dielectric layer, such as ultra-thin oxide, between the first and second electrodes. A programmable resistance, or other property, is established by stressing the dielectric layer, representing stored data. Embodiments of the memory cell are adapted to store multiple bits of data per cell and/or adapted for programming more than one time without an erase process.