Simulation computations represent a very effective tool for investigating operational characteristics and behaviours of vehicles without having a real product. The rail vehicles sector is typical, in that simulation computations including multibody modelling of individual vehicles (i.e., wagons) as well as entire trainsets are widely used. In the case of designing rail vehicles, running safety and ride comfort are two of the most important assessment areas. The presented work is focused on the research of the dynamical effects of a rail vehicle while running on a railway track created in a commercial multibody model. There is a lot of research focused on the investigation of dynamic performances while a rail vehicle is running on a flexible railway track. The real operation of a rail vehicle meets problems on track, where the stiffness-damping parameters of a railway track vary in transient sections (e.g., the exit of a tunnel). This work brings a contribution to research related to the assessment of the dynamic response of a rail vehicle on a chosen track section. A passenger railway vehicle is chosen as a reference multibody model. Simulation computations were performed for three different railway track models, i.e., for a rigid track model and for a flexible track model defined in two different manners. The stiffness-damping parameters of the rail vehicle are defined symmetrically in relation to the longitudinal axis of the vehicle, e.g., they are the same values for the left and right side. The centre of gravity is not located symmetrically, but it is partially shifted in the lateral direction. This can be observed in the results of wheel forces and their waveforms. There are evaluated values and waveforms of the vertical wheel forces, the lateral wheel forces and the derailment quotient. The obtained results have revealed the influence of the railway track formulation in the model on the output parameters.