As is well-known, at present, those calculation formulas on damage and crack produced in materials and structures under monotonous or fatigue loading, which mathematical models are mainly obtained by means of experiments. Author is based on the genetic concepts similar in life sciences, to adopt common parameters and material constants nbfs,,,and ',','nfs in mechanics and engineering materials, to adopt mathematical methods, as variables with the crack and the damage , thereby proposes a series of mathematical models (formulas). For which are: aD The threshold value of damage and the threshold size of crack; the transition value and the thDthatrD transition size between two stages; the critical values and the critical sizes corresponded to those tra critical stresses; the damage value and the crack size under different loading; the strength iDia calculation)'(, and the strength standard])[(where also there are the evolving rate and the life prediction dNdadNdD/,/),(NNfor which are from microscopic, nanometer to macroscopic sizes on damage or crack, that may be one stage, or two stages, or three stages in whole process. On the other hand, for those key parameters in calculating formulas can all giveout theories explains and specific physical and geometrical definitions. In addition, also provides comprehensive curves corresponded to calculation models related material behaviors at each stage towhole process