We present solutions for statistic moments of deformations and stresses in phases of quasi-periodic composite. We use a singular approach for the method of periodic components for the case when statistic moments of deformations and stresses are results of random displacements of centers of inclusions out from cites of ideal periodic grid. In the method of periodic components, structural factors common for a periodic structure and a random quasi-periodic structure are taken into account using corresponding solution of a boundary value problem for a periodic medium. At that, statistical peculiarities of a quasi-periodic structure (for instance, the fact that inclusions are located related to each other randomly) are taken into account considering a solution of a stochastic boundary value problem. The method presented allows us to employ well-established methods for boundary value problems for periodic structures in collaboration with peculiar stochastic methods of the mechanics of composite materials.