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New techniques have been developed to make materials with a periodic three-dimensional lattice structure. The high stiffness per unit weight and multifunction of such lattice structures make them attractive for use in aeronautic and astronautic structures. In this paper, epoxy-soaked continuous carbon fibres were first introduced to make lattice composite structures, which maximize the specific load carrying capacity. A micromechanical analysis of several designs, each corresponding to a different manufacturing route, was carried out, in order to find the optimized lattice structure with maximum specific stiffness. An intertwining method was chosen and developed as the best route to make lattice composite materials reinforced by carbon fibers. A sandwich-weaved sample with a three-dimensional intertwined lattice structure core was found to be best. The manufacturing of such a composite lattice material was outlined. In addition to a high shear strength of the core and the integral manufacturing method, the lattice sandwich structure is expected to possess better mechanical capability.