A theoretical model for progressive solidification is described. It reproduces the experimental finding, from centrifugal wave tank testing with viscous scaling, that a layer of liquefied sand solidifies progressively from the base up while severe fluid-wave loading is imposed over a prolonged period of time. The solidification process reestablishes a grain-supported framework in the transitory fluid-like soil and is accompanied by the marked densification and gradual dissipation of excess pore pressures in a zone immediately below the upward-advancing solidification front. The continued disturbances to liquefied soil in the form of wave loading are an effective means for loosening the interlocking of solid particles, and permit rearrangement into a state of remarkably dense compaction due to contractancy. These aspects of soil behaviour are accentuated through comparison with consolidation in quiescent conditions following liquefaction. Furthermore, the proposed rigorous treatment of solidification as a moving-boundary problem provides a basis for reappraisal of an expression that was presented by Florin & Ivanov regarding the velocity of the solidification front.