Motivated generally by potential applications in the liquid crystal display industry [8,35], and specifically by recent experimental, theoretical and numerical work [6,7,13,14,21,25,30,31], we consider a thin film of nematic liquid crystal (NLC), sandwiched between two parallel plates. Under certain simplifying assumptions, laid out in £2, we find that for monostable surfaces (i.e. only a single preferred director anchoring angle at each surface), two optically-distinct, steady, stable (equal energy) configurations of the director are achievable, that is, a bistable device. Moreover, it is found that the stability of both of these steady states may be destroyed by the application of a sufficiently large electric field, and that switching between the two states is possible, via the flexoelectric effect. Such a phenomenon could be used in NLC display devices, to reduce power consumption drastically. Previous theoretical demonstrations of such (switchable) bistable devices have either relied on having bistable bounding surfaces, that is, surfaces at which there are two preferred director orientations at the surface [7,14]; on having special (nonplanar) surface morphology within the cell that allows for two stable states (the zenithal bistable device (ZBD) [4,21], or, in the case of the Nemoptic BiNem technology [11,19], on flow effects and a very carefully applied electric field to effect the switching.