The conservative system can be described by using Hamilton system and its main feature is symplectic preservation, so conserving the symplectic structure of the system is the most important features. Based on the analytical structural mechanics, the project will establish symplectic algorithms for applied mechanics. Firstly, the project will establish and improve the basic theories of analytical structural mechanics, and broken through the traditional constraints of the time difference scheme and construct a set of space-time finite element sequences with higher precision and better stability for numerical analysis of conservative linear and non-linear system. Secondly, through the research of symplectic perturbation for potential energy and mixed-energy, the project will establish symplectic matrix perturbation method based on the canonical transformation and the matrix multiplication which will provide rich and better numerical analysis method with effective performance for the short-wave approximation and parameters identification problem and will begin the preserving structural theories and application research for the high oscillation problem. Finally, the project will establish high-precision and highly efficient algorithms for some special functions which will lay a solid foundation for the numerical integration of nonlinear systems and give effective analysis tools for the optimal control system with time delay. This research of the project will develop the traditional analytical mechanics to the analytical structural mechanics level and promote symplectic mathematical methods of applied mechanics on the basis of Hamiltonian system.