Cosmic ray variations due to changes in the magnetosphere are evaluated for severe magnetic storm on 20 November 2003 using data from the worldwide neutron monitor network and the global survey method. From these results the changes in the planetary distribution of magnetic cutoff rigidities during this disturbed period are obtained in dependence of latitude. A correlation between Dst index and cutoff rigidity variations was defined for each cosmic ray station. The maximum changes in cutoff rigidities occurred while Dst index was around -472 nT. Geomagnetic effect in cosmic ray intensity reached at some stations 6--8%, and it seems to be the greatest one over the history of neutron monitor observations. The latitudinal distribution shows a maximum changes at geomagnetic cutoff rigidities around 7--8 GV. This corresponds to unusually low latitudes for maximal effect. Cutoff rigidity variations were also calculated utilizing the last model of Tsyganenko for a disturbed magnetosphere (T01S). A comparison between experimental and modeling results revealed a big discrepancy at cutoff rigidities less than 6 GV. The results on the geomagnetic effect in cosmic rays can be used for validating magnetospheric field models during very severe storms.