Understanding and minimising eddy current stresses is of major importance in the design of Fusion in-vessel components. These stresses determine often the life of components since the frequency of plasma disruptions may be a significant portion of the plasma pulses. Careful choice of the component support geometry can result in reducing stresses considerably. This is particularly true with large copper tiles installed inside the Vacuum Vessel as in the JET Neutral Injection (NI) Ducts. The low copper resistivity results in large eddy currents and particular care has to be exercised to minimise stresses. The aim of this work is to define the optimum position of component support points to minimise the eddy current stresses. The components are idealised with linear or non-linear beam models depending on the eddy current force distribution. Then the position of the maximum value for the bending moment as a function of the support locations is estimated in order to obtain minimum moments and therefore stresses. It is shown that a factor of up to approximately 30 in stresses can be gained by careful choice of support positions. The near optimum location is independent of the component material, orientation, size and type of disruption. Should there be geometrical difficulties in using the optimum locations, the effect of different support positions on stresses is quantified. This work has been applied specifically to the design of the JET NI Duct tiles. It resulted in negligible stresses in the inconel support subframe and minimum stresses in the copper tiles. Although the detail analysis restricts itself to in-vessel tiles, the principles are general and the results can be applied to all in-vessel components which normally can be simulated with beam theory.