Forward and reverse current-voltage (I-V) characteristics of commercial rectifying Schottky diodes (SDs) based on silicon carbide (4H-SiC, base layer doping level 3·1015 cm-3) have been studied under irradiation with 0.9 MeV electrons and 15 MeV protons. The starting diodes were characterized by a barrier height of ~1.5 eV and nearly ideal forward and reverse I-V characteristics. It was found that, at doses exceeding the threshold dose Dth, the series differential resistance Rs of the diodes grows as Rs ~ Dm (m = 10-15) and shows no tendency toward saturation. Dth ≈7·1015 cm-2 under electron irradiation, and Dth ≈ 4·1013 cm-2 in the case of irradiation with protons. Heating to 200oC results in that Rs decreases with activation energy of ~1.1 eV and Rs is partly annealed-out with activation energy of ~0.7 eV. The starting Schottky diodes changes only slightly under irradiation, but, possibly, the irradiation leads to an over-compensation of the n-type layer and formation of an additional barrier in the form of a pn junction.