Coherent Anti-Stokes Raman Spectroscopy (CARS) and Coherent Anti-Stokes Hyper-Raman Spectroscopy (CAHRS) are widely used in the study of molecular interfaces and biological membrane surfaces. However, forsuchahigher order nonlinear optical process, the number of molecular microscopic polarization tensor elements areso larger and the relationships is so complexthatthe quantitative analysis of CARS and CAHRS is more difficult. In this paper, we present the simplified scheme for microscopic hyperpolarizability tensor elements of CARS and CAHRS. First, the CARS microscopic hyperpolarizability tensor elements βi′j′k′l′ are expressed as the product of the differentiation of Raman microscopic polarizability tensor α′i′j′. Then the CAHRS microscopic hyperpolarizability tensor elements βi′j′k′l′m′ are expressed as the product of the differentiation of Raman microscopic polarizability tensor α′i′j′ and the differentiation of hyper Raman microscopic polarizability tensor β′i′j′k′. The ratios between the βi′j′k′l′ and the ratios between the βi′j′k′l′m′ are then obtained from the ratios of α′i′j′ and the ratios of β′i′j′k′. Using these relationships between the microscopic hyperpolarizability tensor elements of CARS and CAHRS obtained in this paper, the generalized orientational functional and generalized orientational parameters of CARS and CAHRS are obtained and ready to be used for quantitative analysis of interfacial molecular orientation information.