The mechanics of layered elastic system is a branch of elasticity. Firstly, the development history of layered elastic system mechanics is introduced. Secondly, the mechanical analysis and calculation of $N$-layer elastic system are introduced, including basic assumptions, expressions of stress and displacement components, definite solution conditions, establishment of linear algebraic equations for solving integral constants according to definite solution conditions, solution of integral constants by linear algebraic equations, calculation of Bessel function, integral calculation formula, numerical integration, subsequent mechanical calculation and calculation examples. Finally, the application of layered elastic system mechanics in scientific research and engineering design is introduced.