By using the analog cascade elliptic filters design method, and the bilinear method of transforming analog filters to digital filters, and the frequency transformation method of digital filters, a simple robust cascading digital IIR filter is designed. The stability of this filter can be assured by setting rational frequency transformation parameters. The internal magnitude bound of this filter can be minimized by using an empirical optimal method of poles and zeros organization. At the end of this paper, an example of designing a cascading digital elliptic band stop filter is provided.