Ultracold atoms trapped in optical lattices interact through the dipole -dipole interaction potential that takes place through the photon exchange of the electromagnetic vacuum field. In this paper we propose a method based on Floquet’s theory to determine matrix elements of the dipole -dipole interaction in 3D optical lattices. Numerical calculations are displayed for the case of 1D optical lattices. Bragg dispersion occurs for elastic scattering when the momentum transfer between the interacting atoms in the lattice is a primitive reciprocal lattice vector. The higher dipole -dipole interaction matrix elements correspond to elastic scattering without spin flip and to case when the Bragg condition is satisfied.