The local demagnetizing fields on the surface of flat cylindrical samples (disc) are measured by means of the free radical electron paramagnetic resonance for several thickness-to-diameter ratios from 0·01 to 0·15 and at two values of the external magnetic field (around 4 and 14 kOe). An empirical expression for the demagnetizing field intensity is found and anisotropy of the demagnetizing field is detected in the sample plane. The experimental results are compared with the conclusions of the theory of Joseph and Schlomann.