A memory unit is disclosed in which a planar array of thin film magnetic rod structures is sandwiched between a pair of magnetic sheets. Solenoid windings wound along the length of the rod structure serve as word windings and conductive wires disposed perpendicular to the rod structures and between the sheets serve as digit windings or the plurality of bistable magnetic storage elements formed along the rod structures at the intersections of the conductive wires. The magnetization of each of the storage elements is axially switched to a predetermined one of its two stable states by simultaneously passing appropriate currents through the relevant solenoid winding and conductive wires. A plurality of such units are assembled together to form a threedimensional memory matrix. In constructing such a memory a number of magnetic sheets are placed side by side and a plurality of unbroken conductive wires are laid in grooves in the sheets each of the wires running across all the sheets. The memory is then formed by appropriate folding of the conductive wires and the sheets with the magnetic rod structures sandwiched between the sheets and the conductive wires acting as hinges.