In this paper, construction of complex composite multi-grid finite cuboid elements with heterogeneous and micro — heterogeneous structures is presented.The procedure for constructing complex multi-grid elements reduces to construction of a system of embedded composite two-grid finite elements. Both fine and coarse embedded grids are used to construct a double-grid element. Fine grid is generated after discretization of the double-grid element with consideration of its structure. Coarse grid is defined over the whole area of the element. Coarse grid approximations project the total potential energy functional of the double-grid element with base descretization on a coarse grid. Equations for calculating stiffness matrix and vector of nodal forces are obtained by functional minimization procedures for the energy functional. Consideration of heterogeneous and microheterogeneous structures is one of the advantages of composite multi-grid elements. It is used for developing discrete models of small three-dimensional composite solids and obtaining solutions with specified errors. Thus, stresses can be estimated for every component of heterogeneous structure of composite multi-grid finite elements.