Abstract：By means of selecting elliptical crack model to simulate the defects in quasi-rock materials，the damage model for quasi-rock materials under multiaxial stress state is developed on the basis of hypothesis of the weakest link and statistical fracture theory. The model displays the interaction of the failure of rock，the stress state，the cracks in the rock and the material¢s coefficients. According to the equivalent hypothesis of strain，a constitutive relation containing damage model is established. At last，the following conclusions can be drawn：(1) the greater the friction factor of the crack¢s plan is the greater the strength of quasi-rock material is；(2) because of the friction between the crack¢s plans under multiaxial compressive stress states，the greater the confining pressure is the greater the strength is；and the stress-strain curve changes from linear curve into nonlinear curve；(3) the bigger the modulus m in Weibull¢s model of the material is the less the strength is. These conclusions are in a good accordance with the current study results.
