Since the time of D'Arcy, the study of the flow of fluids through packed beds of particles has used a convenient analogy from electrical theory. Resistivity, or its inverse, permeability is ascribed to the bed and, at low Reynolds numbers at least, this property is sufficient to describe the behaviour of flow. However, the permeability of a bed is not the fundamental property that electrical resistivity is and it is necessary to relate it to a more fundamental property of the system if it is ever to be possible to exercise predictable control over it. In this thesis, the relationship between the permeability of a bed and the particle size distribution of its constituent particles is considered. A literature review is presented which surveys all the attempts which have partially succeeded in producing such a relationship. A new theoretical model, based on the mean pore diameter and tortuosity is derived which relates the permeability of a bed directly to its particle size distribution. Experimental measurements of permeability are presented and compare well with the model in some cases. In other cases, the bed is found to be unstable and the permeability of the bed is itself influenced by the flow of fluid. The reasons for the instability of the bed are discussed.