After the recent devastating tsunami in southern Asia, I tried to find a simple way to present the physics of this phenomenon to students—in particular, the origin of the dispersion relation and the consequent wave properties. Being unable to locate a suitable source for a truly elementary approach, I developed the simple derivation presented here by extending to shallow-water waves a clever capillary wave model recently developed by Behroozi and Podolefsky (2001 Eur. J. Phys. 23 225). The main properties of tsunami waves can thus be obtained with an elementary and straightforward procedure suitable for undergraduates in physics and other disciplines.