Summary: This paper presents a three-dimensional consolidation model, based on mixture theory. Both the Eulerian and the Lagrangian formulations are given in one dimension for finite strain and general material nonlinearity. Then the paper formulates the initial-boundary value problems related to several situations of relevant geotechnical engineering interest, such as consolidation between draining and impervious boundaries subjected to stress and/or velocity conditions, consolidation under own weight of a layer growing due to deposition of wet material, or to sedimentation of solid particles in a quiescent fluid.