This paper presents the development process of a fully-coupled multiphysics finite-element model of electromagnetic tube compression, using the commercial software Comsol Multiphysics. The presence of a field concentrator inside the solenoid coil is numerically modelled. First, the results of free compression of a S235 steel tube are presented. Next, the joining process of a S235 steel tube with an internal workpiece of the same material is considered by inclusion of a contact algorithm in the model. Simulation results are compared with available experimental data. The application of the model to materials with a high resistivity, such as steel, enables to identify interesting phenomena and opens new possibilities for the industrial application of this high velocity forming technique.