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ITER is a magnetic confinement fusion experimental reactor (TOKAMAK), planned to be built in France (Cadarache). The scope of ITER is to demonstrate the scientific and technological feasibility of fusion energy for peaceful purpose. The Divertor is a fundamental "in-vessel" component of the ITER machine. The main function of the Divertor system is to exhaust the major part of the alpha particle power as well as helium and impurities from the plasma. As the main interface component under normal operation between the plasma and material surfaces, it must tolerate high heat and electro magnetic loads while at the same time providing neutron shielding for the vacuum vessel and magnet coils in the vicinity of the Divertor. The research activity of this Ph.D. has been focalized mainly on two topics that represent "the pillars" of the entire work. The first topic concerns the methodology and a possible approach to the problem of set up the acceptance criteria for the tiles of CFC (Carbon Fibre Composite) of the Divertor at the start of life of the ITER machine. A study on the reliability and the applicability of this method as well as a possible statistical approach to the definition of the acceptance criteria are addressed in this thesis. The second topic is the developing of a user-friendly software, inside a commercial, certificated and very well documented finite element code like ANSYS, able to evaluate the evolution of the erosion in the CFC tiles of the Divertor. The evaluation of the speed of erosion of the CFC (Carbon Fibre Composite) tiles is very important to evaluate the longevity of those components. Moreover, the software developed will be an important tool for the final definition of the acceptance criteria for the tiles of CFC.