Urban railway vehicles are important means of transport in towns and cities due to their high capacity, power source, and low running resistance, which make them efficient for operation. Although these properties are considered advantages, there is still room for improvement in their operational efficiency. The main objective of this article is to investigate the impact of railway wheel design on the level of kinematic running resistance, which is expressed as the amount of mechanical energy losses during the interaction of wheels with rails. This research focuses on simulation computations of two variants of wheel design schemes: the traditional design scheme (TKS) and a perspective design scheme (PKS) characterized by a rotating flange independently of the wheel tread surface. Two undercarriage multibody models have been created, one with TKS and one with PKS, and simulation computations have been performed for running speeds of 10 km/h, 20 km/h, 30 km/h, and 40 km/h on track models in curves with radii of 20, 50, 100, 150, 200, and 250 m. The evaluated indicators affecting the level of mechanical energy losses were creep forces, slip velocities, and average power. The most important findings of this study are that the PKS design scheme resulted in lower values of all assessed parameters.