Based on analytic structural mechanics, the interface of the two nearest substructures extends to a region with a certain width, named interbelt, where the interbelt theory and the corresponding algorithm under the framework of symplectic system can analyze the nonlocal characteristic of structures. The integral of time delay elasticity system in analytic dynamics still has many questions in theoretical aspects, which needs to be made clear. There are simulative relations between analytic dynamics and analytic structural mechanics, hence the interbelt theory can be applied in solving the integral problems of time delay elasticity system, and the corresponding arithmetic can be founded based on symplectic system. Numerical examples were carried out for the validity of the theory and algorithm developed. As a basic research work, the present study illustrates well the potential of the interbelt as well as the symplectic algorithm and is valuable for the further research.