The model problem proposed to study the buckling of stratified geological layers consists of a linearly elastic plate, capable of accommodating finite rotations, resting over an inviscid and buoyant fluid. The Lyapunov–Schmidt–Koiter decomposition is applied to construct the bifurcated equilibrium solutions. The asymptotic analysis of the post-buckling reveals a decrease in the magnitude of the lateral compressive force during an overall shortening of the stratified structure. Buckling and post-buckling are not influenced by the presence of a vertical stress gradient in the elastic plate.