From an available solution for the deformation of elliptical holes in a viscous material, a criterion is developed for fracture by the growth and coalescence of cylindrical holes under any prescribed history of applied principal components of stress and strain which do not rotate relative to the material. The criterion is extended to plastic materials by extrapolation from an analysis for the growth of circular holes under equiaxial transverse stress. Experiments on Plasticine substantiate the analysis and its extrapolation. For both plastic and viscous flow, most of the applied strain to fracture is found to occur while the holes are still small compared with their spacing. The most striking result is that in plastic materials there is a very strong inverse dependence of fracture strain on hydrostatic tension. The theory also indicates the effects of anisotropy, strain-hardening, and strain gradients on ductile fracture by the growth of holes.