AbstractSimulations of crack growth that are based on the cohesive surface methodology typically involve ill‐conditioned systems of equations and require much processing time. This paper shows how these systems of equations can be solved efficiently by adopting the domain decomposition approach in which the finite element mesh is partitioned into multiple blocks. The system of equations is then reduced to a much smaller system of equations that is solved with an iterative algorithm in combination with a powerful two‐level preconditioner. Although the solution algorithm is more efficient than a direct solution algorithm on a single‐processor computer, it becomes really attractive when used on a parallel computer. This is demonstrated for a large scale simulation of crack growth in a polymer using a Cray T3E with 64 processors. Copyright © 2001 John Wiley & Sons, Ltd.