A theory to describe transient and static equilibrium profiles in sedimentation and filtration is proposed. The dynamic aspects are based on Darcy's law and a continuity requirement in Lagrangian coordinates, recognizing that the Darcy flux describes flow of liquid relative to the particles in response to a space gradient of liquid potential. The equilibrium profiles may be calculated when the space gradient of liquid potential is zero. The theory is restricted to materials where the particle size distribution is such that no sorting of particles occurs.