The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. In this paper, we consider the parallel complexity of generic pairwise elimination, special cases of which include Gaussian elimination with pairwise pivoting, Gaussian elimination over a finite field, generic Neville elimination and Givens reduction. We develop a new block-recursive, communication-efficient BSP algorithm for generic pairwise elimination. © 2006 Elsevier Ltd. All rights reserved.