Abstract: This paper elucidates the necessity of introducing differential geometry in the quantitative study of structural geology and discusses its applications in the quantitative study of structural geology and relevant numerical calculation method.Differential geometry provides a basis for the quantitative description of the geometry of geological structure and construction of a precise mathematical analytical model and is also an important mathematical tool for the indepth quantitative study of the geometry of geological structure and its variations.In order to combine differential geometry with other advanced techniques and methods more conveniently,on the basis of previous studies,the authors summarize the construction and reconstruction of a mathematical model for geological structure,computer-aided automatic analysis and calculation and 3D visualization and movement simulation.It can be applied to the forecasting of fractures,analysis of structural plane deformation,morphological classification of folds,detection of hidden faults and evaluation and study of mineral deposits and oil/gas accumulations.