Abstract: Ferromagnetic shapememory alloy (FSMA) is a new class of functional material. Inaddition to the general behaviors of traditionaltemperature-controlled and stress-controlled shape memory, FSMAcan produce large strains under an external application inmoderate magnetic fields. This ability makes FSMA suitable for awide range of applications. This paper reviews the research onmechanical behaviors of FSMA. It focuses on the study of themechanical behavior, and also includes the topic of theapplication of the materials. It summarizes the effects of thecrystal component, the magnetic field, the stress, and thetemperature on the mechanical behavior of the material. It alsosummarizes the developments of a constitutive model forferromagnetic shape memory alloy.