Topological indices(TIs) are important numerical number associate with the molecular graph of a chemical structure/compound because due to these parameters, one can guess almost all properties of concerned structure/compound with our performing experiments. In recent years, huge amount work has been done for calculating degreedependent indices for different structures/compouds. In order to compute TIs, one need to do many calculations. Our aim of this paper is to present a simple method to compute degree-dependent TIs. We computed M-polynomials for Block Shift Networks and with the help of this simple algebraic polynomials, we recovered nine important TIs for Block Shift Networks. Our work is important for chemists, physicians and pharmaceutical industry.