For a very small void in the material between much larger voids the influence of local stress increases induced by the larger voids is studied numerically. The point of interest is whether or not such local stress increases result in a cavitation instability at the tiny void, even if the average overall stress levels are well below those required for unstable cavity growth. The analyses are based on an axisymmetric unit cell model with special boundary conditions, which allow for a relatively simple investigation of a full three dimensional array of spherical voids, without having to solve the full 3D numerical problem. For overall stress levels as large as those reached ahead of a blunting crack tip, a cavitation instability at the small void, induced by interaction with the large voids, is not found here. But the results show that localization of plastic how in the unit cell plays an important role. (C) 1998 Elsevier Science Ltd. All rights reserved.