The capillary rise of liquid in a cylinder bank is examined in order to study the capillary pressure variation perpendicular to the direction of the cylinders. The calculations consider the local geometric variation of the flow channel and the position-dependent capillary pressure. The capillary flow around each cylinder is calculated by balancing the capillary pressure and the viscous drag along the flow path. The rate of filling for several layers of cylinders is used to estimate the equivalent capillary pressure. The method is also applied to the underfill of a flip chip system, which is modeled as a cylinder bank between parallel plates. (C) 2003 Elsevier Inc. All rights reserved.