Magnetoelastic buckling and postbuckling of ferromagnetic rectangular plates with geometric nonlinearity in magnetic fields are quantitatively investigated in this paper. A numerical program combining the nonlinear finite element method with an iterative method is proposed to solve the twofold nonlinear problem. The numerical results show that the ferromagnetic plate buckles when it is in a transverse magnetic field, and it bends prior to its instability when it is in an oblique magnetic field with tiny incident angle. The deflection pattern of the plates is changed from one-wave to semiwave after they lose stability.