The plane contact problem on the transfer of loading from a periodically arranged elastic finite pads to two identical elastic strips with initial stresses is solved using the linearized theory of elasticity. The study is carried out in a general form for the theory of large initial deformations and different variants of the theory of small initial deformations for an arbitrary elastic potential. The effect of the initial (residual) stresses on the distribution of the contact stresses over the interface with the periodically arranged elastic finite pads is investigated.