In this paper the authors present a new one-dimensional phenomenological model of the magnetic shape memory effect (MSME) observed in magnetic shape memory alloys (MSMAs). The model takes into account elementary processes associated with the magnetisation of MSMAs. Its correctness has been checked against selected models known from the literature. The model developed by the authors has been verified in the case of a rod element made out of a MSMA by the use of the finite element method (FEM). A study on the influence of activation of MSMA beam actuators in the case of forced vibration of a composite beam has been performed. The authors have also carried out investigation connected with the influence of a transverse and open crack on the effectiveness of vibration reduction in the case of a composite beam by the use of MSM actuators.