In present paper the inverse problem on the identification of three non-homogeneous residual stress components in rectangular plate in steady-state vibration regime is considered. The equation building the iterative process of solving the inverse problem is formulated. An approach to the reconstruction of residual stresses is described on the basis of introduction the Airy prestress function. The technique of leading the inverse problem to a system of linear algebraic equations at each iteration is proposed. Results of conducting a series of computational experiments on the reconstruction are depicted and discussed.