The hydrostatic stress in compliant rubber inclusions embedded in a rigid polymer matrix is evaluated for various shapes and orientations of the rubber domains and triaxialities of the remote stress tensor to determine the propensity of the inclusions to undergo cavitation. The first section analyzes the case of rubber particles of an ellipsoidal shape assuming linear elasticity of the matrix and small strains. It is shown that flat shapes, of which the long axis lies perpendicular to the direction of the maximum principal stress, are subjected to the highest levels of hydrostatic stress. The pressure induced by the deviatoric part of the remote stress tensor in the compliant rubber domains depends strongly on their shape and orientation, whereas the pressure induced by the hydrostatic part of the tensor is almost insensitive to the shape and orientation of the compliant domains. The second section examines the stress concentrations for elastoplasticity and plastic dissipation in the matrix. It is found that spherical inclusions ensure the best compromise between the early occurrence of plasticity and large amounts of plastic dissipation. (C) 2004 Wiley Periodicals, Inc.