The theory of moving packets is developed, and a practical moving packet model for Richards' equation is created, implemented using linked lists, and verified for vertical flow in variably saturated layered porous media. The model uses a Lagrangian approach. When simulating infiltration, for example, packets of water are injected at the ground surface, and an implicit finite difference approximation to Darcy's law is used to track the vertical movement of the boundaries which separate each packet from its neighbors above and below. In effect, the boundaries define a nonuniform self-adapting grid which is carried along with the flow. The moving packet method was designed to be used as the basis for models of coupled flow, transport, and mixing. Its advantage is that transported properties and matter can be carried within the packets, simplifying the modeling of advection, dispersion, and mixing. ¿ 2000 American Geophysical Union