One model of random media is presented according to the theory of spectral factorization in stochastic process and Hudson's model of cracked medium. The advantage of Hudson's model is to make contact between the crack's micro-parameters (crack number density) with the macro-properties (elastic constants) of cracked media. Using this advantage, we present an ellipsoidal random model. The results show that the model outline the relationship between micro-properties and the macro-properties of random media, and can flexibly and effectively describe real cracked media, and the crack number density has different effect on the elastic constants of random cracked media.