The behaviour of beds of fine-grained sand under fluid wave trains was investigated using centrifuge modelling. Three sets of centrifuge wave tank tests with viscous scaling were performed, such that time-scaling laws for wave propagation as well as consolidation were matched. The test programme consisted of either progressive- or standing-wave tests on loosely packed, fresh deposits of soil, as well as repeated travelling-wave tests with intervening periods of consolidation. The results from the progressive- and standing-wave tests indicate that for each of the wave-loading regimes, there exists a critical cyclic stress ratio below which Liquefaction does not occur. The critical value for the progressive-wave-loading series was found to be considerably smaller than that for the standing-wave-loading series. Moreover, the wave-induced liquefaction of the sand beds was of a progressive nature. In fact, under the action of severe travelling waves, liquefaction was first induced in the uppermost layer of the sand bed, and then the liquefaction front advanced downward in the course of wave loading, eventually bringing the entire soil bed into a state of complete Liquefaction. It is also shown from the repeated wave tests that the liquefied beds of soil underwent significant densification in the consolidation processes that followed. In each of the subsequent wave-reloading stages, re-liquefaction was observed to occur in such a way that the final depth of the liquefaction front became shallower.