Capillary rise experiments were performed in columns filled with glass beads and Berea sandstones, using visual methods to register the advance of the water front. For the glass bead filled columns, early time data are well fitted by the Washburn equation. However, in the experiments, the advancing front exceeded the predicted equilibrium height. For large times, an algebraic behavior of the velocity of the front is observed (T. Delker et al., Phys. Rev. Lett. 76, 2902 (1996)). A model for studying the capillary pressure evolution in a regular assembly of spheres is proposed and developed. It is based on a quasi-static advance of the meniscus with a piston-like motion and allows us to estimate the hydraulic equilibrium height, with values very close to those obtained by fitting early time data to a Washburn equation. The change of regime is explained as a transition in the mechanism of advance of the meniscus. On the other hand, only the Washburn regime was observed for the sandstones. The front velocity was fitted to an algebraical form with an exponent close to 0.5, a value expected from the asymptotic limit of the Washburn equation. Copyright 2001 Academic Press.