The storage unit comprises an array of tunnel tips (13) arranged at tunneling distance from a recording surface (2a) of a storage medium (2) which is capable of permitting digital information to be written or read through variations of the tunneling current. The storage medium (2) is attached to the free end of a piezoceramic bendable tube (3). In operation, the free end of the tube (3) is moved in a circular orbit by repetitive sequential energization of oppositely arranged pairs of 90.degree. phase shifted electrodes (4,6 and 5,7). This tube movement causes each tunnel tip (13) to scan a respective unique associated annular area of the storage medium (2). To address a particular concentric track in a particular annular area, tunneling current is applied to the associated tip (13) via respective electrodes (16,18) while, concurrently, a potential is applied via electrodes (4,6 and 5,7) to tube (3) of a magnitude corresponding to the desired orbital diameter for the tube.