The critical load required for a rigid, flat punch to cause failure of a material obeying the linear Coulomb-Mohr yield criterion in plane strain is bracketed by upper and lower bound values determined by plastic limit analysis. These values are a function of the cohesion and angle of internal friction of the material, the inclination of the free surface from the horizontal loaded surface, and the placement or "indexing" distance of the load from the free surface. Theoretical failure paths indicating possible volume removal of the material under critical loading by the flat punch are postulated and compared with actual failure paths observed in damp sand model experiments at atmospheric conditions.