Abstract: In long-distance water diversion and urban water supply pipelines, operational events such as system start-up, shutdown, and transitions can induce water hammer effects. 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. Addressing the issue of water hammer in elastic pipelines, this study considers uncertainties that are difficult to express in actual pipelines, including the nonaxial movement of the