The allowed electromagnetic modes in the presence of a symmetric array of macroscopic bodies are investigated. They are systematically classified by their behaviour with respect to the different symmetry operations. In the presence of two bodies the modes are required to be even or odd, in the presence of lattices Floquet's theorem is applied, The van der Waals (vdW) energy of the array under consideration is calculated from the average quantum energy of the electromagnetic modes. Since finite boundary conditions are used, no difficulties regarding branch points and different Riemann surfaces are encountered. Closed expressions for the vdW energy in periodic lattices of spheres or cylinders are obtained which can be explicitly evaluated at a reasonable rate of effort.