Abstarct: Water quality undergoes significant changes during conveyance through transmission pipelines due to complex physical, chemical, and biological processes. One such process that has attracted researchers' attention in recent years is the sudden intrusion of contaminants due to transient flow. When a negative pressure wave from water hammer reaches points of structural failure such as leaks, it leads to the sudden suction of contaminants from the pipe's surrounding environment into the internal flow, which can jeopardize public health. Understanding the complex process of sudden contaminant intrusion and its influencing factors requires an accurate and optimized modeling approach to estimate the amount of intruded contamination. This research, through precise numerical modeling of a reservoir–pipe–valve system with a leak, baxsed on Eulerian and Lagrangian approaches, aims to estimate the quantity and dispersion pattern of contaminants entering the pipe due to transient flow. The hydraulic flow equations were solved using the Eulerian Method of Characteristics (MOC) and the Lagrangian Wave Tracking Method (EWTM), and the contaminant transport equations were solved using the Eulerian Extended Period Simulation (EPS) and the Lagrangian Event-Driven Method (EDM). This study introduces an Eulerian-Lagrangian numerical solver in MATLAB software capable of systematically quantifying contaminant intrusion while considering the interaction of pressure wave fluctuations. A comparison of computed contaminant intrusion volumes with experimental data shows a normalized Root Mean Square Error (nRMSE) of 4.53% for the Lagrangian method and 5.96% for the Eulerian method, confirming the accuracy of the hydraulic and leak modeling. Contaminant dispersion under transient conditions was modeled using the Lagrangian method, and a comparison of the results with the Eulerian method shows high accuracy with a maximum nRMSE of 5.5%. The results indicate that the volume of contaminants entering a viscoelastic pipe is significantly reduced compared to elastic pipes. Results from a comprehensive sensitivity analysis involving 36 different scenarios show that the relative pressure head along the pipe is the most influential factor on the volume of contaminant intrusion. The maximum rate of contaminant re-extrusion was observed near downstream valves, reaching approximately 68%; whereas the middle sections of the pipe recorded the highest amounts of contaminant intrusion and trapping. These findings indicate that although the effect of contaminant re-extrusion can be significant under specific conditions, it can be neglected for greater conservatism in design/analysis. The results also show that employing the Lagrangian numerical solution method offers, on average, over 80% better computational efficiency compared to the Eulerian method.