We report the results of a detailed geometrical and electrical study which has been performed on aYBa2Cu3O7−δ superconducting whisker. This sample has undergone three subsequentsteps of micro-machining by means of a focused ion beam (FIB)instrument, in order to progressively decrease its cross-sectional area from∼77 to∼4 µm2, over a lengthof about 150 µm. A simple analytical model based on the exact shape both of the electrical contacts and ofthe micro-machined material has been proposed for the voltage drop; besides,an accurate geometrical characterization of all of the sample details has beenperformed by means of SEM microscopy. This enabled us to extract accurateelectrical resistivity curves from the resistance versus temperature characteristics foreach of the fabrication steps of the whisker, showing an increase of the sheetresistivity with decreasing cross-sectional area. Among the possible physical reasonsfor such behaviour, inelastic electron scattering at the sample surfaces has beenruled out because of the very short mean free path of carriers in YBCO. Onthe other hand, oxygen out-diffusion and Ga ion implantation due to the FIBprocessing are most likely to be responsible for the observed resistivity trend.