In this work, volume of fluid (VOF) technique, one computational fluid dynamics (CFD) method, was used to investigate the upward Taylor flow in vertical square and equi-triangular capillaries. For saving computation time, the simulations were carried out in a moving frame of reference attached to Taylor bubbles. The main flow parameters, involving bubble size and shape, liquid film thickness, velocity field and two-phase relative velocity, were studied as functions of capillary number. The numerical simulations were in good agreement with previous reports and showed that the flow in the sides and corners of polygonal capillaries were different. A comparative study was also conducted on Taylor flow in square and equi-triangular capillaries and their circular counterparts, where the influence of capillary geometry on the characteristics of Taylor flow was illustrated clearly. (C) 2007 Elsevier B.V. All rights reserved.