The problem of a steady, axisymmetric, fully developed adiabatic bubbly flow in a vertical pipe is studied analytically with the two-fluid model. The exchange of momentum between the phases is described as the sum of drag, lift, wall and dispersion contributions, with constant coefficients. Under these conditions, we are able to express analytically the void fraction profile as a function of the liquid velocity and pressure profiles. This relation is valid independently of the Reynolds stress model in the liquid phase- and can serve as a verification case for multiphase flow codes. The analytical void fraction profile vanishes at the wall, as a result of the balance between dispersion and wall forces. It presents a peak near the wall for upward flows, whereas its maximum is reached in the center of the pipe for downward flows. This is illustrated by calculations performed for upward and downward bubbly flows with the NEPTUNE_CFD code. (C) 2016 Elsevier Ltd. All rights reserved.