The main objective of this work is to study the possibilities of improving the running safety of a railway wagon with independently rotating wheels by changing their design symmetrically mounted on an axle. The article provides a discussion of the advantages and disadvantages of using the independently rotating wheels in a bogie of railway wagons. Their increasing tendency of derailment is described. The influence of a perspective constructive scheme (PKS) of railway wagon wheels in comparison with a traditional constructive scheme (TKS) on running safety due to the climbing of a wheel flange onto a rail is studied. This work introduces a conceptual proposition of a technical solution to railway wheel design as well as containing the results of both analytical calculations as well as the results of multibody simulations. A PKS wheel design for a railway wheel is designed that allows independent rotation of its tread surface and of a guiding surface (i.e., of a flange) to each other, which both are arranged symmetrically on a wheelset axle. It brings features of the distribution of friction forces generating in a flange contact when the wheel with a TKS and with PKS move on a rail. It is possible to conclude with the help of the obtained results that the use of wheels with the PKS is advisable for the reduction of the running resistance as well as for increasing the running safety of railway wagons.