This article is devoted to solving urgent problems related to the development of a mathematical model and methods for assessing the dynamic characteristics of railway wheelsets. In the simulation, railroad wheelsets are considered as a one-dimensional deformable body based on the Bernoulli-Euler theory with two rigid disks. The cross-section of the shaft is assumed flat and perpendicular to the centerline during vibration. Disks are modeled as a rigid body characterized by mass and moment of inertia. The centrifugal and gyroscopic effects and the damping properties of the material are taken into account. With these factors, the problem under consideration is reduced to a higher order of a homogeneous system of differential equations, which is then solved using the Altair Hyperworks and Matlab software. The dynamic characteristics of railway wheelsets are investigated depending on the angular speed of the wheel (without taking into account the contact between the wheelset and the rail), with and without damping. At that, a number of new mechanical effects were established.