The understanding of the lift force, which governs the lateral migration of bubbles, is important to improve closures for continuum flow models that are used to simulate large-scale dispersed gas-liquid flows. In the present work, the effect of bubble size/shape and more importantly the effect of neighboring bubbles on the magnitude and direction of the lift force were investigated. The rise behavior of single/multiple bubbles in liquids of different properties imposed with linear shear was simulated by using the VOF method. The predicted lift coefficients (C-L) for single bubbles rising in sheared viscous liquid (corresponding to the ellipsoidal regime, 2.35 <= Eo <= 11.68, log Mo = -5.3) were compared with the measurement of Tomiyama et al. [2002. Transverse migration of single bubbles in simple shear flows. Chemical Engineering Science 57, 1849-1858]. Further, the lift force acting on single bubbles rising in low viscosity liquid (corresponding to the wobbling regime, 1.1 <= Eo <= 8.72, -10.6 <= log Mo <= -14.6) was investigated. Unlike the steady lateral migration of single bubbles with a single characteristics value of C-L (+ve or -ve depending on d(B)) for viscous systems, the bubbles were found oscillate around the center line and the instantaneous C-L was found to fluctuate in both +ve and -ve directions. The effect of neighboring bubbles on the lift force was investigated by simulating the rise of six homogeneous (mono-dispersed) and heterogeneous (poly-dispersed) bubbles in a viscous liquid. It was observed that individual bubble wakes led to increased bubble-bubble interaction and as a result fluctuations in C-L were increased. The time-averaged C-L of all the bubbles was found to be very small as compared to the characteristic C-L obtained for the single bubble rise. These observations confirm the hypothesis of Beyerlein et al. [1985. Prediction of bubble concentration profiles in vertical turbulent two-phase flow. International Journal of Multiphase Flow 11, 629-641] and Behzadi et al. [2004. Modelling of dispersed bubble and droplet flow at high phase fractions. Chemical Engineering Science 59, 759-770] that C-L approaches to a very small value with moderate increases in the volume fraction. (C) 2009 Elsevier Ltd. All rights reserved.