Based on Kalker’s three-dimensional elastic rolling contact theory, the influence coefficient and the normal distance in the minimum complementary energy function were modified, making it proper for solving non-planar contact problems. Using the modified contact model, the wheelrail normal contact characteristics at 30 t axle load was studied with a 100 million gross traffic tonnage of CHN75 profile worn rail and an LMA original profile wheel. The results show that the wheel-set lateral displacement has a significant impact on the contact characteristics. Remarkable changes of contact state can be seen at +12mm to +14mm. Twopoint contact occurs at +12.9mm to +13.2mm, and the contact between wheel flange and rail gauge corner occurs at +14mm.