In order to simulate the real medium underground more correctly, this paper puts forward a new method of local random position or given position arbitrary shape intercepting combined with multiscale random modeling technology. From the existing theory of the random modeling, the local disturbing position is given in the effective modeling area and this position is taken as the central point of each disturbing distribution. Two model characteristic quantities, namely the local disturbing radius R and the local random or given disturbing angle , are introduced, and all sorts of different random medium models are simulated by the method of local position arbitrary shape intercepting and filled with each random medium. This paper presents basic steps and application examples of the model.