A molecular memory medium for storing digital bits at a density of several hundred million per square centimeter. The medium is read and written by a tunnelling probe, and comprises a plane surface and a means for moving the surface relative to the tunnelling probe. Arrayed on the surface are plural memory elements, each storing one bit, and having, relative to the surface, a first positional state and a second positional state, representing the first state and the second state, respectively, of the bit. The positional states are distinguished from one another by a difference in a tunnelling current in the tunnelling probe. The memory element is switched from one positional state to the other by an electrostatic force applied by the tunnelling probe. A molecular memory apparatus for reading such a molecular memory medium includes a tunnelling probe, a drive for moving the storage medium relative to the tunnelling probe, and a controller for positioning the tunnelling probe relative to the track and the surface. A voltage applying circuit applies a voltage to the tunnelling probe, and a circuit causes the voltage applying circuit to apply a first voltage to the tunnelling probe and measures the resulting tunnelling current that depends on the positional state of the memory element adjacent to the tunnelling probe. Finally, a circuit determines from the tunnelling current the digital state represented by the memory element adjacent to the tunnelling probe, and provides the determined digital state as an output bit.