A filter cake can be described as a porous media with a complex system of interconnected interparticle voids. The objective of this investigation was to perform the generation and description, in 3D, of capillary ducts in four different porous media (cakes) of the spheres obtained by means of simulation. A computer program was developed for the random generation of the capillaries through the voids of the simulated cakes. The results indicated (a) significant variation of the diameter of the capillary ducts as a function of the height of the cake. That is correlated with the segregation observed in simulated filter cakes; (b) the average of the calculated length of capillaries presents small variations for all the simulated structures; (c) the values of the average of the superficial area and volume of the capillaries are bigger for Samples B and D when compared with the Samples A and C indicating differences in the transport capacities; (d) there is not significant variation in the parameters values when the number of generated capillaries is increased; (e) the values of calculated permeability are qualitatively in agreement with the filtration results obtained at laboratory; (f) further studies are necessary for the knowledge of the complex transport of fluid (liquid and/or gas) through the generated capillaries in the simulated cakes. (c) 2005 Elsevier Ltd. All rights reserved.