Water hammer (WH) is a critical phenomenon in fluid-filled piping systems that can lead to severe pressure surges and structural damage. The characteristics of the pipe material, geometry, and support conditions play a crucial role in the fluid–structure interaction (FSI) during WH events. This study investigates the impact of various pipe parameters, including material, length, thickness, and diameter, on the WH behavior using an FSI-based numerical approach. A comprehensive computational model was developed based on the algorithm presented in Delft Hydraulics Benchmark Problem (A) to simulate the WH phenomenon in pipes made of different materials, such as steel, copper, ductile iron, PPR (polypropylene random copolymer), and GRP (glass-reinforced plastic). This study examines the influence of pipe parameters on WH performance in pipelines, utilizing FSI to analyze the phenomenon. The results show that the pipe material has a significant influence on the pressure wave speed, stress wave propagation, and the overall system response during WH. Pipes with lower modulus of elasticity, such as PPR and GRP, exhibit lower pressure wave speeds but higher stress wave speeds compared with steel pipes. Increasing the elastic modulus, pipe wall thickness, length, and diameter enhances the pipe’s stiffness and impacts the timing, magnitude of pressure surges, and the likelihood of cavitation. The findings of this study provide valuable insights into the design and mitigation of WH in piping systems.