In this work, mass transfer at the shell side of an in-line hollow fiber array subjected to cross-flow is simulated by applying the domain decomposition method combined with orthogonal grid generation. Two-dimensional Navier-Stokes equations written in stream function-vorticity variables, were separately solved along with a species conservation equation for different arrays. The main factors influencing the concentration fields, local mass transfer rates and global mass transfer rates in the laminar flow of Re = 10-200 and Pe = 10-300 with pitch to tube diameter ratios of 1.45, 1.50, 1.75, 1.85 and 2.00 are discussed in detail. Mass transfer correlations obtained from the numerical simulations show good agreement with typical empirical correlations proposed earlier. (c) 2004 Elsevier Ltd. All rights reserved.