Background <p>The carbon nanotubes (CNTs) reinforced magnetostrictive sandwich material combines carbon nanotubes with magnetostrictive layers in a sandwich structure. It takes advantages of both carbon nanotubes and magnetostrictive materials on magneto-mechanical performance.</p> Purpose <p>In this study, the nonlinear vibrations and stability of a CNTs-reinforced composite magnetostrictive plate interacting with subsonic airflow and resting on an elastic foundation are explicitly investigated.</p> Methods <p>The equations of motion of the plate are derived using Hamilton’s principle in conjunction with the assumed mode method. By computing the natural frequencies, the validity of the proposed dynamic model is confirmed.</p> Results <p>The effects of the face-to-core thickness ratio, elastic foundation stiffness coefficients, CNT volume fraction, and velocity feedback control parameters on the stability of the plate are discussed. The amplitude-frequency response and displacement–time history are further exhibited to illustrate the nonlinear resonance properties of the plate. The vibration suppression effects contributed by the magnetostrictive layers are also presented.</p> Conclusions <p>The findings of the present paper provide theoretical insights for stability design in practical scenarios.</p>