This paper presents an analytical method, namely interface stiffness transfer method, for evaluating the responses of multilayered elastic structures. Based on the Love function and general solutions, the stiffness matrix relationship of the displacement-stress state vectors is introduced to obtain the interface stiffness transfer matrix equation between adjacent layers, which satisfies an algebraic Riccati matrix equation. When the elastic layer is a half-space, an explicit solution is obtained directly for the interface stiffness matrix. The interface stiffness transfer matrix method starts from the bottom layer with a known stiffness, and then deals with one layer at a time until the uppermost layer is reached, obtaining the interface stiffness of the multilayered structure. Finally, by solving the symmetric equilibrium equations of the boundary conditions, the displacement-stress state vector of an arbitrary layer is obtained. This method keeps the advantages of the classical transfer matrix method, but naturally excludes its exponential growth terms. In particular, the proposed method is a powerful candidate for efficiently solving the algebraic Riccati equation for the optimal control problems. Numerical examples show the properties of the interface stiffness transfer method.