A composite structure includes a grid having filaments built up in a stacked arrangement in rows with the rows crossing at nodes where the filaments of the crossing rows are interlaced. None of the filaments passes directly through any node, but instead the filaments of each row pass to the sides of a central area in the node with half being on one side of the central area and half being on the other side. The filament lay-up around the nodes is such that only two filaments cross at any one location thus equalizing filament build-up at the nodes and webs. The stacked array of filaments is impregnated with a resin, which may be applied to the filaments before or after the lay-up, and the resin upon being cured forms a hard matrix in which the filaments are embedded. Preferably, the rows of filaments assume three different orientations, with those orientations being at 60.degree. angles with respect to each other. Moreover, at each node the rows of all three orientations intersect so that the rows delineate voids having the shape of equilateral triangles. The grid may be flat, substantially flat, or concave or it may be tubular. Other orientations for the rows of filaments are possible.The filaments of a flat grid structure may be laid into place with a computer controlled plotting or drafting machine fitted with an applicator head which passes over a surface area having pin-like nodal elements arranged in rows corresponding to the rows for the filaments. The applicator head includes a needle and a supply of filament, with the latter being threaded into the former and emerging therefrom at the surface area. The plotter moves the applicator head such that its needle moves along the rows of nodal elements, and as it does, the filament pays out of the needle. The filaments for a tubular grid structure may be laid into the crossing rows by a machine which braids, wraps or winds the filaments about a mandrel and between the nodes. The mandrel outwardly from the nodal elements is provided with rotatable orienting pins which deflect the filaments to the proper sides of the nodal elements.