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The laws of applied mechanics can be used to analyze and predict the behavior of mechanical parts subjected to strain and distortion, such as endodontic instruments. Simple mathematical formulas can be used to represent the impact of torsional and bending inertias on stresses in endodontic instruments being used in root canals. The boundary integral method was applied to two theoretical models with the same diameters but different cross-sections to evaluate quantitatively and qualitatively the stresses produced in orthogonal cross-sections. The results confirmed the mathematical deduction concerning the impact of torsional and bending stresses. The results indicate that clinical protocols based on the torsional and bending properties of endodontic instruments must be strictly followed, and endodontic instrument manufacturers must adopt standardized criteria for describing these properties.