An interlocking support structure has an array of rectangular cells arranged in at least one layer, each cell having four sides, opposite ends, and eight corners, and sharing common sides and corners with any adjacent cells. The cells are formed by sets of spaced, parallel elongate members extending in x, y and z directions, with the x, y and z members interlocked with one another at the corners of the cells to form interlocking corner joints. Each structural member is hollow at least in the vicinity of each corner joint with which it intersects, and communicates with the other structural members at the respective corner joints. A plug of hardened, initially flowable material fills the hollow interior of the interlocking structural members at least at the corner joints and adheres to the internal surfaces of the members at the corner joints to secure the members together at each corner in the rectangular array.