Composite plates have the advantages of high strength and light weight and are widely used in the field of aerospace engineering. Instability is their most common failure mode. Considerable research on the instability of composite plates under linear loads has been conducted, but there is less research on the instability of composite plates under nonlinear loads. Therefore, an instability discriminant model for a metal composite plate under a nonlinear load is established using a metal composite plate as the object of study. The influence of width, thickness, thickness ratio, and material properties on the discrimination factor of instability is analyzed. Analysis results show that, for common metal composite plates with aspect ratios four, under the same load, larger ratios of width to thickness, smaller elastic moduli, and larger Poisson's ratios of each layer of the plate make the plate more prone to instability. Under the premise of the same total load, compared with the linear uniform load, the composite plate is more and more prone to instability with the increase of the nonlinear load. These conclusions serve to supplement theoretical results.