In the pulp and paper industry, it is often necessary to characterize the drainage capability of a pulp on the paper machines. The industry uses a standard measure called the freeness to represent this and other properties for papermaking pulps.The freeness is the total volume of water discharged from a side orifice of a specific configuration while the pulp suspension drains freely under gravity. In this paper, a model for the gravity filtration of pulp suspensions forming a compressible pulp mat is along with some empirical treatment of the flow is used to model the freeness test. The gravity drainage process is assumed to be described by a cake filtration process with the pressure at each instant being given by the gravity headFrom the model, the critical parameters governing the freeness of a pulp suspension are shown to be the specific surface area and the specific volume of the pulp fibers in addition to the compressibility of the pulp mat. When these parameters are available from independent gravity drainage measurements, the freeness itself can be estimated. Estimated freeness values are in agreement with experimental measurements for pulps which are reasonably free of fines. When fines are present however, they get entrapped within the pulp mats decreasing their permeability. The model predictions are higher than experimental measurements in this case.