The thin film composite often buckles due to mismatch strain between each layer induced by in-plane residual stress during manufacturing or service loadings in operation. The buckling behavior of a composite structure consisting of a thin film and a compliant substrate was studied by elastic stability analysis based on complex function theory. The buckling parameters under uniaxial and biaxial in-plane compression were calculated respectively utilizing an author compiled program. The result indicates the critical pre-buckling stress is an inherent characteristic determined by material and geometric parameters. Under uniaxial and non-equal biaxial compression stress,the critical pre-buckling stress decreases with the increase of film/substrate elastic modulus ratio,meanwhile there is only one nonzero buckling wave number in the direction of the plane. For the equal biaxial stress,the influence factors of critical pre-buckling stress and dimensionless wavelength depend on substrate/film thickness ratio. Any buckling mode that satisfied with the wave number equation could occur.