The short-term uptake of a fluid by porous media is important in a number of processes, such as in coating and printing operations. We present a new model to predict short-term absorption into real pore geometries taking into account fluid properties, surface forces, and the complex pore geometry. Two assumptions are made to reduce the complexity of the situation: (1) the flow resistance between pores can be estimated from pore geometry or air permeability measurements, and (2) the volume of fluid in the constrictions between pores is small. Pores can be connected in any manner and can be in any arrangement. The absorption rates predicted by the model are compared to experimental values obtained with coating layers of plastic, kaolin, and calcium carbonate pigments. These coatings are characterized in terms of void fraction, pore size, contact angle, and permeability. The comparison is good for water and inks when the air permeability of the porous layer is used to determine the average resistance to flow in the sample. These resistance values are close to the values obtained from pore geometries estimated from particle packing simulations.