A special kind of magnetic shield, called the “magnetic cloak” consists of two parts: superconducting insert and ferromagnetic shell. In the numerical modelling utilized e.g. for the design and optimization purposes, electromagnetic behaviour of both these materials should be properly included. A similar situation exists also in case of conventional superconducting power devices like transformers and motors. The implementation of A-formulation in COMSOL Multiphysics allows building a numerical model that considers in the same physics the superconducting material and the ferromagnetic one. An important feature is that the Jiles-Atherton model of magnetic hysteresis could be easily implemented. In this way, the interaction between superconductors and ferromagnetic material can be introduced directly in the computation. We present numerical and experimental results for the magnetic cloak, where the superconducting part is made from six layers of coated conductor (CC) tapes and the ferromagnetic one is from an epoxy/ferrite powder composite. The current distribution in superconducting tapes and the magnetization of the ferromagnetic shell are solved within the same physics using the A-formulation.