In recent years, anchored-frame structures are widely being used in road slopes for stabilization and improvement. The technology of frame structure with anchors is becoming more and more mature, but the pertinent theory lags behind the application. While more attention is being paid to the control of deformation, there is still no uniform solution to the calculation of deformation in the anchored-frame structures. According to the classical laterla earth pressure theory and static equilibrium, this paper improves the calculation method of lateral earth pressure and derives the calculation formula of slope-induced lateral earth pressure. At the same time, based on the elastic foundation beam model, the columns and beams are treated as a whole system, and the appropriate elastic frame beam model is established. The formula of the deformation and bending moments for the columns and beams in the anchored-frame structures are derived. Additionally, the calculated results based on the abovementioned newly derived formulas are compared with those of finite element simulations for a simulated case study. The results of simulation and analytical calculation are basically consistent, which prove the feasibility of the new analytical method.