A stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non-Sibsonian interpolation. In this approach, both the shape functions and the integration scheme are defined through use of first-order Voronoi diagrams. The method illustrates improved performance and significant advantages over previous natural neighbour formulations. The method also shows substantial promise for problems with large deformations and for the computation of higher-order gradients. Copyright © 2004 John Wiley & Sons, Ltd.