Synopsis At the tip of a sharp crack or re-entrant notch, the stresses calculated by a simple elastic analysis become infinite. Consequently, maximum-stress or -strain failure criteria and stress-concentration factors cannot be used to predict failure at such points. The linear elastic fracture mechanics theory can, however, be applied. In the paper, a brief treatment of the application of this theory to sharp cracks in concrete beams is presented and the effect of beam size is particularly examined. The same basic technique is applied to re-entrant notches. Experimental evidence of the validity of the approach is given. Theoretical results are included which allow these test data to be extended to a wide range of notch conjigurations. It is expected that this work will have considerable importance for the problem of crack initiation at corners of openings in walls etc.