A numerical study, using the volume-of-fluid method, has been made of vertical (upward) laminar core-annular flow: the flow of a high-viscosity liquid core surrounded by a laminar low-viscosity liquid annular layer through a vertical pipe. The numerical results are compared with theoretical results from linear stability calculations and with experimental data. The comparison is good and the general conclusion of our study is that it is very well possible to simulate laminar core-annular flow in a pipe using the volume-of-fluid method. VC 2014 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.