Fracture initiated from a sharp crack or wedge shaped notch in a homogeneous material, subjected to different loading is considered. Singularities in the stress fields at edges and vertices are discussed. A point-stress criterion is used to predict fracture for sharp cracks as well as 90° wedge notches in expanded PVC foam. The point-stress criterion is formulated in a manner allowing failure predictions in general 3D stress situations. The influence of non-singular T-stress at cracks is discussed and substantiated by experimental results.