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This work has moved from the idea of using finite element (FE) analysis as a general tool for thermal noise studies relating to improve the performances of interferometric gravitational wave antennae.On the one hand, a complete model of an actual Virgo mirror has been done to perform Brownian thermal noise calculations through the numerical dynamic approach. The analysis is performed including, in one model only, all the ancillary components on the mirror. The mesh of the coating is user-driven, allowing the creation of relatively simple models on which parametric analyses can be run.On the other hand, in the framework of research of new suspension materials for future interferometric antennae, a facility for measuring Q on crystalline silicon fibres through the ring-down technique has been realized. The data obtained by a dedicated apparatus to measure the fibre profiles are used to create FE models. FE analyses allow to find the resonance modes helping the Q-measurement procedure and FE parametric analyses allow to extract Young’s modulus.