In this paper, a theoretical model is developed to describe a magnetic force arisen from an interaction between the nonlinear magnetization of structures made of soft ferromagnetic materials and an applied magnetic field in which the structures are placed. The fundamental equations of ferromagnetic structures in a magnetic field involve twofold nonlinearity since the interaction between the magnetic field and the deformation of the structure leads to the equations nonlinear besides the nonlinear magnetization. Magnetoelastic bending and buckling of a simply supported rectangular plate, as an example, are investigated by these fundamental equations. A numerical programme combined the 3D FEM with the iterative method is suggested to quantitatively simulate the magnetoelastic behavior of the plate. It is found that the characteristics of magnetoelastic bending and instability for the plates having nonlinear magnetization are distinctive from those of the plates having linear magnetization.