The Swift X‐ray Telescope (XRT) is designed to make astrometric, spectroscopic and photometric observations of the X‐ray emission from Gamma‐ray bursts and their afterglows, in the energy band 0.2–10 keV. Here we report the results of the analysis of Swift XRT Point Spread Function (PSF) as measured in the first four months of the mission during the instrument calibration phase. The analysis includes the study of the PSF of different point‐like sources both on‐axis and off‐axis with different spectral properties. We compare the in‐flight data with the expectations from the on‐ground calibration. On the basis of the calibration data we built an analytical model to reproduce the PSF as a function of the energy and the source position within the detector which can be applied in the PSF correction calculation for any extraction region geometry. All the results of this study are implemented in the standard public software.