Magnetic and mechanical behaviour are strongly coupled in ferromagnetic materials. An accurate description of these coupling phenomena can be key to the design of electromagnetic sensors, actuators or transducers. This chapter details a modelling approach to predict the magneto-elastic response of a ferromagnetic material subjected to complex multiaxial magneto-mechanical loadings. The model relies on a multiscale approach for the description of the anhysteretic behaviour, and on an energy-based vector-play approach for the description of dissipative mechanisms. The model is able to predict the macroscopic response under simultaneous variations of stress and magnetic field. The validation of the whole approach is made by comparison to experimental results obtained on a low-carbon steel.