The imbibition of water or other liquids in a fiber web is a dynamic and transient phenomenon. At any time during the process there exists a non-uniform distribution of fluid in the spatial dimensions of the fiber web, and this distribution varies with time. The fiber web is a porous medium with pores of different sizes. The analogy of fluid imbibition diffusion-type transport process has been commonly suggested in literature; it is used here to describe the phenomenon. By experimentally measuring the key parameters of the fiber web (specifically the flow conductivity and the relationship of capillary pressure versus equilibrium saturation), it is possible to determine the diffusivity coefficient, and the fluid distributions at different times can be calculated by the diffusion equation. An example of wicking of water by a pulp fluff web is also discussed. -- AATA