AbstractDelaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication or important serialized parts. In this paper, we propose a method that achieves high speed‐ups, but needs information regarding locally maximum element circumspheres prior to the beginning of the algorithm. Such information is directly available in iterative methods, like the particle finite element methods. The developed parallel Delaunay triangulation method, has minimum communication requirements, is quite simple and achieves high parallel efficiency. Copyright © 2007 John Wiley & Sons, Ltd.