Abstract This paper addresses the problem of one-dimensional solidification of concentrated mixtures of solid particles in a Newtonian host fluid. This problem has ramifications in the fields of sedimentation and filtration, and is presently studied in the context of restabilization of liquefied cohesionless soils. Solidification is described in terms of a wave phenomenon, and its propagation and structure are modeled in terms of conservation of mass and momentum principles and the necessary constitutive relations for closure. Relative motion between the two species as well as variations in volume concentration of the granular material are taken into account. The solution yields the distributions of the solids stress, solids concentration, pore pressure and component velocities below the solidified interface. The thickness of the shock over which these adjust from their liquefied to their solidified values is found to be sensitive to the particulate material properties. On the basis of this study it is suggested that measuring the local pore pressure gradient in a cohesionless soil yields more useful information on the state of the soil than commonly used single pore pressure transducers. It is further shown that controlled laboratory experiments on solidification wave propagation can be used as a practical way of determining the properties of the particulate material.