An experimental and analytical study was made on the effect of stress singularities on the strength of expanded PVC foam materials of different densities. Experiments were performed on specimens with different wedge geometries ranging from sharp cracks, with the ordinary inverted square root stress singularity, to shallow re-entrant corners with weak singularities. A brittle fracture criterion based on a generalised stress intensity factor, called Q, at the wedge tip was fit to experimental data. The critical stress intensity factor, Qcr, for crack initiation depends on the wedge geometry. This dependence was estimated from simple point-stress criteria and a criterion due to Seweryn [Brittle fracture criterion for structures with sharp notches. Engng Fracture Mech. 47, 673-681 (1994)], and good agreement with experimental data was obtained. When the point-stress criterion was applied to Mode II sharp cracks, poor agreement with published data was found. A critical study of the Mode II crack specimen was therefore initiated, leading to the conclusion that the commonly used specimen gives erroneous values of KIIc and the reason seems to be due to crack surface friction. A new Mode II crack specimen which eliminates crack surface friction was proposed and tested, and good agreement with the point-stress criterion was obtained. A criterion for homogeneous materials proved to be adequate also for the porous PVC foams.