The work aims to study the surface buckling of rectangular orthotropic anisotropic film/substrate system with finite length and width under unidirectional compression. The critical strain and the evolution of post-buckling morphology were analyzed by Kirchhoff-Love thin plate theory and von Kármán plate theory, and the anisotropic properties of materials and the influence of geometric parameters of thin films on surface buckling were investigated. Generally speaking, the initial buckling of the film/substrate system always happened with multiple wrinkles. Previous research demonstrated that the number of wrinkles varied with be change of the film width under the same film length. When the anisotropy of the film was very strong, the film/substrate structure showed some remarkable characteristics. One of them was that the edge amplitude increased with the rise of the film width after the applied strain exceeded the critical buckling strain, while the center amplitude decreased sharply. This phenomenon makes the difference between the edge amplitude and center amplitude larger and larger, ultimately leading to sharp change of post-buckling morphology in the width direction and indicates that other buckling pattern may appear in the width direction with the increase of the applied strain.