Abstract: In pressurized water transmission pipelines such as long-distance water diversion and urban water supply systems, operational events such as system start-up, shutdown, and transitions can induce water hammer effects, leading to pipeline structure damage and even pipe bursts. Therefore, accurate and efficient hydraulic transient calculation is crucial for system hydraulic safety and intelligent regulation and control. However, the existing hydraulic calculations are mainly based on the traditional elastic water hammer theories, which tend to overlook and underestimate uncertainties related to energy dissipation and pressure attenuation. In addressing the issue of water hammer in elastic pipelines and aiming to enhance the precision and reliability of computations, this study considers uncertainties that are difficult to express in actual pipelines, including the axial movement of the fluid, the anchoring constraints of the pipeline, and the inertial effects of the fluid. Two water hammer models tailored for elastic pipelines are proposed: a coupling model integrating the generalized Kelvin-Voigt model with from the Zielke unsteady friction model, and a water hammer model based on the generalized Kelvin-Voigt model. Both methods allow for parameterization of creep functions through time-domain full waveform inversion methods. In order to substantiate the accuracy of the models discussed in this paper, an experimental setup was meticulously assembled to simulate the water hammer phenomenon. The results show that the coupled model can effectively improve the accuracy of transient simulation of water hammer in elastic pipelines, but its efficiency is relatively low. In contrast, the generalized Kelvin-Voigt model significantly increases the computational efficiency of both the simulation and the inversion of creep functions, while still maintaining high accuracy. Through error analysis, it can be concluded that the derived creep functions are applicable to other experimental conditions within the same pipeline system. Therefore, this study provides a precise and efficient computational approach for water hammer analysis.