The problem of the determination of the effective behaviour of a linear elastic random heterogeneous material is considered anew in the more general situation of the analysis of a structure made of such a material. Macrohomogeneous conditions make the scale transition possible. The connection between both scales operates through a representative volume element with finite extension and with well-known shape. A global Hashin and Shtrikman variational formulation leads to rigorous formal bounds on the effective moduli, which can be made explicit for a composite exhibiting an ellipsoidal distribution of the phases.