The bilayer structure with hard upper layer and soft lower layer is widely used in many fields, and these applications have raised considerable interests in recent years. The two modes of compressive buckling instability, deformation mechanism, and evolution law of the bilayer structure need to be studied in depth. To solve these problems, the following research was carried out. Based on the pre-stretching method and thermal induction method, the ordered one-dimensional wrinkle structure and disordered random wrinkle structures was experimentally prepared in the Au/PDMS and Au/PS bilayer structure surfaces, and surface morphology, cracks, and interface were characterized. Based on the nonlinear Von Karmen plate theory, the buckling behaviors of bilayer structure was analyzed. The two modes of compressive buckling with and without delamination of the interlayer interface between film and substrate is studied for the bilayer structure using finite element numerical simulation. The results reveal that the amplitude and required load of bilayer structures have the same evolution laws with compressive strain under the conditions of interface delamination and non-delamination.