Background. The development of haptic touchscreens, that is touchscreens with the ability to mimic the feel of a real keyboard, would be a significant advance in the mobile phone and tablet market. This report investigates one possible route to developing such touchscreens using piezoelectric actuators placed at the edge of the screen and driven at a range of frequencies. Scope. The report addresses the following questions: Can an array of piezoelectric transducers placed round the edge of the screen create localised vibrations in the right physiological range to produce the sensation of a keyboard? If so how many transducers are needed? Where should they be placed? How should they be driven? We consider both the excitation of longitudinal and transverse waves but do not discuss surface waves. Methods. We first consider the full inverse problem in which a key shaped vibration is to be constructed by driving a touchscreen embedded in a phone. We argue that a useful subproblem is to construct a localised vibration in a one dimensional beam driven at one end. If such solutions do exist, that would (1) provide strong evidence that solutions to the full inverse problem do exist, (2) act as good initial starting points towards solutions of the full inverse problem. Results. We show that in the case of longitudinal waves the mathematical formalism set up for sonar can be exploited. In the case of transverse waves the system is highly dispersive and so a ready-made formalism does not exist. However we show that localised solutions can likewise be constructed. Conclusions and Recommendations. Our results suggest that it is indeed possible to construct virtual keyboards by driving the edges of a touchscreen. The minimum number of transducers needed is two although we expect that using more would increase resolution. However, before a practical implementation can be made there is still a great deal of work to be done both on the simplified models and on the full problem.