In this report, we address the problems of water hammer and transient phenomena in water-filled pipes. Indeed, water hammer and vibrations cause troubles and damages on hydraulics installations. Here, we report a numerical approach to understand and avoid the problems inherent to these two phenomena. A Method Of Characteristics (MOC) computational model was used to study the resonance frequencies within the pipe and their location. We investigated the parameters that influence vibration and transient phenomena in pipelines and more specifically in sea outfalls and we studied the pressure response in time and frequency domain. In a first step, we defined a typical pipe to be studied in our experiments. Then we adapted an open-source MATLAB MOC code that runs simulations to our typical pipeline with several outlet conditions. The code was compared and validated with Allievi software in a tank-pipe-valve-tank system to simulate water hammer and verifying the code that we adapted. Finally, we included a coastal wave spectrum in the code to simulate sea waves at the pipe's outlet. With this project, we showed the link between resonance frequencies for the three first mode of vibration in function of several input parameters and the location of the pressure peaks within the pipe and the levels of pressure at resonance. The peak frequencies inside the pipe can be as large as 95 times the excitation pressure.