Abstract：Considering different micro-structure of rock，random non-homogeneous thermal elastic mechanics model and FEM based on this model are put forward. Numerical stimulation in made for plane stress state to study the influence of thermal dilatability on thermal cracking law and temperature threshold，and only thermal dilatability is considered as random variable and thermal dilatability is of uniform distribution，Gauss distribution and Weibull distribution. Stimulations show that relationship between temperature threshold and thermal dilatability of uniform distribution is a line function，relationship between temperature threshold and thermal dilatability of Gauss distribution is a power function，and relationship between temperature threshold and thermal dilatability of Weibull distribution is a power function.
