Introduction: Currently, mobile boom cranes equipped with telescopic boom equipment are widely used in construction, loading and unloading, as well as installation. Purpose of the study: We aimed to develop a dynamic model for a railway lifting crane, taking into account the interaction of its structural elements with each other and the bearing soil surface in a three-dimensional formulation. Methods: In the course of the study, we used Simulation and Motion modules of the SolidWorks software package, Klepikov’s non-linearly deformable soil model, and Lagrange’s equation of the second kind. Results: As a result, we developed a numerical analytical 3D model describing dynamic loading and deformation of the “mobile boom crane – foundation” system in a three-dimensional formulation. The model takes into account the following: the internal bending deformation and the interaction of the mating structural elements of a crane (telescopic sections, telescoping hydraulic cylinders, and outriggers), hoist rope rigidity, grillage (framework of sleepers) influence, elastic and plastic properties of the base platform soil, and action of inertial loads on the structural elements of the lifting crane.