Fuel rod cladding failure in a nuclear reactor produces different phenomena related to vibrations and fluid–structure interaction. The most significant aspect of those phenomena is the creation of a pressure wave at the failure position and its propagation in the coolant fluid flowing around the fuel rod. An accurate understanding of the propagation of the pressure wave around the fuel rod can help us design a method to detect a failure, determine its position, and estimate some of its characteristics with a single and simple sensor, such as a pressure sensor or a piezoelectric acoustic sensor, that can be mounted relatively far from the failure. Such a method can be useful for the monitoring of nuclear fuel rods, where instrumentation possibilities are restricted (because of neutron flux, radiation, high temperature, and available space) as well as for any kind of application involving annular ducts and limited instrumentation possibilities. The current paper is related to the specific application of nuclear fuel rod monitoring. It deals with preliminary numerical simulations that are necessary to know the evolution of a fluid pressure profile along the system containing the rod. They are carried out by finite element methods, using the EUROPLEXUS code. They provide the necessary information about the propagation of pressure waves around the rod to design measurement and signal processing methods as well as properly interpret experimental results from tests in industrial reactors, research reactors, or experimental mock-ups. They also provide some information that could not be experimentally obtained because of the constraints in a nuclear environment. Despite the specific application we show in this article, similar calculation methods, theoretical observations, and results interpretations can be easily adapted to the other mentioned applications.