Abstract <p>In the work, it is considered the dynamic behavior of a deformable system consisting of a one-dimensional elastic guide (subsystem 1) and a one-dimensional distributed object (subsystem 2) continuously moving along it. A formulation of a self-consistent boundary value problem is given, which correctly takes into account the interaction forces in the area of subsystem coupling. In the case of uniform motion of a distributed object of constant density, an exact analytical solution to the problem of forced oscillations is found. An expression is obtained for the force caused by the wave pressure (the force of resistance to movement). It is studied the dependence of the constant component of this force on the speed of the object and the frequency of the external action. The possibility of reducing the resistance to movement of a distributed object under vibration impact by radiating waves into the guide is established. Next, the problem of vibrations of a rail guide when an extended train moves along it is carried out. A beam lying on an elastic foundation is used as a model of the rail guide, and the train is considered as a one-dimensional medium with zero bending rigidity. It is assumed that during vibrations, a distributed load acts on the beam from the cars. There are presented dispersion curves calculated for different load movement speeds. Critical speeds of its movement are found, upon crossing which the number of flexural waves excited in the guide changes. These speeds depend on the physical and mechanical properties of the guide, load and base. The minimum value of the speed of load movement at which instability of the guide by transverse vibrations occurs is determined.</p>