An elliptical model of cutoff for solar cosmic rays (SCR) at high latitudes has been calculated for SCR events and geomagnetic storms that occurred in February, March, and September 2014, June 2015, and September 2017 in order to predict the polar cap absorption (PCA) effect. The prediction is compared with observations of the PCA effect at the AARI network of six ionosondes, located in the north of Russia in a wide range of longitudes from 30 to 170 and magnetic latitudes from 56 to 64. We examine the dependence of the cutoff latitude on the magnetic storm strength, as well as the effect of additional ionization of the dayside and nightside ionosphere by SCR protons and electrons. The model demonstrates a satisfactory statistical accuracy up to 0.83 for the PCA prediction. We discuss prospects for further improvement of the elliptical model, such as consideration of the impact of SCRs of higher energies and inclusion of the PC index of energy flux into the polar cap.