This paper studies the mechanism, modelling, and applications of deformable magnetized structures under external magnetic fields. These structures, known as "magnetic soft continuum robots" (MSCRs), have become increasingly interesting because they allow advances in the field of intra-corporeal navigation and minimally invasive surgery. Several scientific and technological challenges arise in the design, modelling and control of this new family of soft robots. This paper investigates the modelling of such mechanisms both analytically and numerically. Finally, a series of simulations including various magnetic fields and magnetization configurations of the proposed robotic system are carried out. The preliminary results demonstrate the relevance of this type of robot, and provide a new perspective for the design and optimization of this robot in some targeted applications.