An overdamped three-layer model consisting of two harmonic chains of interacting particles, representing the upper and the middle layers, which move over the substrate potential, is studied in the present paper. A dc+ac force is applied only on the upper harmonic chain, and dynamics of both layers are investigated. The results show that the dynamical mode locking and Shapiro steps appear not only in the upper layer but also in the middle one. It is noted that the motion of particles in the upper layer corresponds to the standard Frenkel-Kontorova model. The dependence of the Shapiro steps of the middle layer on the system parameters are determined. It is shown that the height of the first Shapiro step of the upper layer is unrelated to the interaction parameters of the particles of both the upper and the middle layers, while the height of the first Shapiro step of the middle layer depend only on the interaction parameters of the particles of the middle layers. Two critical forces which transfer from locked state to the sliding one of both the upper and the middle layers are also studied. They depend on the amplitude and the frequency of the external ac driving force.