In this study, the snap-through buckling behaviour of axisymmetric shells subjected to axisymmetric horizontal edge load or edge displacement for various shell parameters and various boundary conditions is investigated. Interesting results, which seem not to have been reported previously have been obtained. An exciting application of edge displacement type of loading is seen in metal - ceramic composite transducers developed by sandwiching piezoelectric (PZT) ceramic between two metal end caps. The metal end caps serve as mechanical transformers for converting and amplifying the lateral displacement of the ceramic into an axial motion normal to the metal cap. Such metal - ceramic composites are utilized as fish finders, hydrophones, actuators, and transducers with integrated sensing and actuating functions. In our numerical search, we have observed that, for the problem under consideration, snap-through and snap-back buckling is possible for a very narrow range of the shell parameter used. Outside this range, we were unable to locate snapping. On the other hand, it was possible to locate a much wider range of the shell parameter in which snap-through buckling occurs when the shallow spherical cap has an opening around the apex. As far as the possible application of these findings in transducer design is concerned, it is necessary to obtain the displacement amplification and the blocking or generative force for various material and geometric properties. The numerical results are presented in graphical forms.