We develop a semianalytic method for the computation of arc-menisci motion in an imbibition process through any irregular polygonal cross section for any arbitrary wetting angle from 0° to 90°. The method produces the sequence of unique arc meniscus configurations that develop as the capillary pressure decreases throughout the imbibition process. To test for robustness of the algorithm, we apply the method to the analysis of arc meniscus motion for imbibition processes in a sample of 23,639 throat cross sections obtained from analysis of X-ray computed tomographic images of 22% porosity Fontainebleau sandstone. Extending the work of Glantz and Hilpert (2011), we define the chord axis, which captures the motion of stable arc menisci in a polygonal cross section. Unlike the one-parameter family of drainage axes introduced by Lindquist (2006), the chord axis is independent of the wetting angle. We demonstrate that the semianalytic method can be used to construct the chord axis for any polygonal cross section.