The Thesis is dedicated to flow-induced vibration studies in high-powered cooling systems consisting of many rigid rods between which water or heavy water (deuterium oxide) flows as a cooling agent. The goal is to determine the impact on dominant frequencies of the two system parameters – rod mass and its mounting stiffness. Due to simplicity, the investigated model system consists of a single, flexibly mounted rod inserted into an array of rigid rods with a triangular arrangement. The moving rod has two degrees of freedom. Both ends of it may move in the direction of flow and perpendicular to the flow. Several series of laboratory experiments have been performed to study in depth the impact of the single moving rod mass, the position in the array and the support stiffness on the amplitude and frequency of oscillations at different flow rates. The experiments were conducted in collaboration with the Paul Scherrer Institute in Switzerland. An analysis of the obtained data showed that the frequency ratio of vibrations caused by natural frequency and turbulence is a parameter that allows detecting changes in the above-mentioned input parameters in indirect way. Computational fluid dynamics (CFD) simulations were performed to study numerically the behaviour of a flexibly mounted rod in the cross-flow. To model the rod movement, it was described as a mass – spring system. In addition, it was analysed how to minimise computing time and costs. The optimal size of the computational domain was found for the given Reynolds numbers. Simulations at different inflow velocities allowed to analytically describe the distribution of the flow field in the gap between two adjacent cylinders introducing inflow boundary conditions for CFD simulations. The impact of the mass and the stiffness coefficient of the flexibly mounted rod on frequencies of the oscillation was assessed using the metamodeling approach. Using data from laboratory and numerical experiments, new second-order and 7-term orthonormal Legendre polynomial approximation models were created. The inverse analysis, which was applied to experimental data, allowed to develop a model describing the relationship between the frequency ratio, the stiffness and the mass. The created approximation models are applicable to the alleviation of uncertainty, monitoring of cooling systems or early detection of damage related to the reduction of the mass of rods or to changes in the stiffness of the supports.