Abstract: A truss structure for use in outer space comprises a plurality of module units and can be deployed into a structure having a flat surface or a curved surface. Each module unit comprises members, two pairs of flexible chords and four diagonal members. The members are arranged along the edges of an imaginary rectangular parallelepiped. The flexible chords of the first pair are stretched in that face of the imaginary parallelepiped which defines the flat or curved face, along the diagonals of this face. The flexible chords of the second pair are stretched in that face of the imaginary parallelepiped which opposes said face, along the diagonals of this face. Each diagonal member is provided in the corresponding one of the other four faces of the imaginary parallelepiped, along one diagonal of this face, extending at right angles to the diagonal member provided in the opposite parallel face.