Abstract：The model of cracked media with crack number density of spatial distribution is presented according to the theory of spectral factorization in stochastic process and Hudson′s model of cracked media. The random distribution of crack number density is characterized by a 2D exponential ellipsoidal function or Gaussian auto-correlation function in this paper. Hudson′s crack model can connect micro parameters of cracks，crack number density, with macro mechanical properties. By taking the advantage of Hudson’s crack model，the real heterogeneous anisotropic medium can be effectively modeled. Numerical example indicates that the random distribution characteriztics can be different for different elastic constants under the same random distribution of crack number density. By changing the value of the auto-correlation length pair，it is possible to model the difference of the distribution in the two coordinate directions. The random media can be modeled with different stochastic characters by choosing different auto-correlation function. In other words，the Gaussian function describes the single-scale，smooth heterogeneous media and the exponential function describes the multi-scale self-similar heterogeneous media.
