In the regional integrated energy system (RIES), the pipeline dynamics in cooling, heating, and gas networks make their source outputs and load demands difficult to balance in real-time. Hence the economic dispatch problem of RIES requires considering the pipeline dynamics to make the results in line with the actual situation. In this paper, the method of characteristics is proposed to solve the approximate analytical solution (AAS) of partial differential equations describing the gas pipeline dynamics, and the corrected parameters in the AAS are identified by the data-driven method. The high computational accuracy of the obtained AAS is verified by an example. Considering the stochastic fluctuation of renewable energy output and the energy storage ability of cooling, heating, and gas pipelines in a RIES, a stochastic multiple energy storage model for the stochastic economic dispatch problem of RIES considering the pipeline dynamics is established. An improved approximate dynamic programming algorithm considering the coupling of power balance among several adjacent time intervals due to the pipeline dynamics is proposed to efficiently solve the stochastic multiple energy storage model. Test results on an actual RIES, including comparison with the scenario-based method, demonstrate the correctness and efficiency of the proposed model and algorithm.