Based on the definition of Lamé coefficient, this paper calculates the Lamé coefficients in the commonly used orthogonal curvilinear coordinate systems, and gives the arc length, panel element and volume element represented by Lamé coefficient. Combined with specific problems, the application of Lamé coefficient in kinematics and analytical mechanics is discussed. Through analysis, it can be seen that the Lamé coefficient reveals the mathematical basis of one kind of physical problems, which is conducive to simplifying the understanding of this kind of problems and reducing the calculation steps. Furthermore, the use of the Lamé coefficient promotes the integration of related mechanics knowledge.