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The aim of this article is to develop the mathematical model to describe response of endodontic file in curved root canal during the preparation of root canal using fracture mechanics approach. Any obturation process involves the filling of prepared root canal using bio-compatible materials like gutta-percha. During preparation of infected root canal, substrate, dead tissue and pulp is removed and tapered shape is formed so that any practitioner can fill it effectively. During preparation process of root canal, the canal wall applies locking action and causes resistance to motion of endodontic file, finally resulting into fatigue failure. This article described plastic behavior of endodontic file in curved root canal, mathematical model describing the necessary condition for crack growth in endodontic file, a mathematical model describing plastic zone size for crack on surface of endodontic file, a mathematical model describing crack tip opening displacement for crack on surface of endodontic file and mathematical model for pure-combined torsion and bending consideration for design of endodontic file. The mathematical model described is helpful for the Endodontic experts, researchers, design engineers. However the applicability of the described mathematical model limited to assumption of study. The gap between root canal to be prepared and endodontic file is zero while preparation. The endodontic file weight, speed of rotation and substrate removal rate is assumed to be constant. The mathematical model for endodontic file discussed above proved to be efficient tool for studying the root canal preparation.