Polar cusps are an essential element of the magnetospheric topology. In the outermost regions of the cusp the magnetosheath plasma becomes entrained on magnetospheric field lines and penetrates to low altitudes along field lines on the dayside, causing a significant local depression of B, clearly visible in magnetometer data taken at high latitudes. This study addresses the spatial distribution of the magnetic depression associated with the polar cusp, as derived from a large set of Polar magnetometer data taken in 1996--1998. The depression ΔB was derived as the difference between the total magnitude of the observed field and the one calculated from the International Geomagnetic Reference Field model of the internal field, combined with an external field model. In the noon sector the cusp depression is clearly visible in plots of ΔB versus solar magnetic latitude as a relatively narrow region of large negative ΔB (down to ~-80 nT), extending from R~8--9 RE (Polar apogee) to R~5--6 RE. At closer geocentric distances the cusp depression fades out because of a rapid increase of the geomagnetic field toward Earth. The cusp depression also shallows as one moves away from the noon meridian and completely disappears at solar magnetic longitudes ¿40--60¿. The second part of the paper deals with a mathematical representation of the observed polar cusp depression in quantitative models of the geomagnetic field. A method is suggested on the basis of the field deformation technique, making it possible to incorporate a realistic structure of the polar cusps in global models of the magnetosphere. ¿ 1999 American Geophysical Union