Abstract: In this paper, based on the basic assumptions of stress damaged beams, simple evolution equations of stress damaged beams under pure bending are derived. The bending damage variable is defined as the reduction of moment of inertia similar to that of tensile damage variable in Kachanov's model which is defined as reduction of loading area. The material's constants of the equations can be determined by Kachanov's tensile damage model. The nature of stress damage failure of beams is discussed in details. For the simplicity of failure prediction in engineering, the evolution law of bending stress damage variable is transformed into a simple form.