A number of rods are disposed along at least three differently oriented axes, the rods being formed by bonding together bundles of fibers with a matrix. Each rod in one group is passed between rods of the other differently oriented groups. The cross-sectional shape of a rod extending in at least one direction is matched to the shape of a clearance which is left between rods extending in other directions to admit the rod inserted therethrough. Put otherwise, a rod extending in at least one direction has a projection to fill such a clearance. Great enough strength to withstand external forces exerted from any direction is imparted to the three-dimensional fabric composite materials either by increasing the area of contact between individual rods or by minimizing the clearances between rods by means of a matrix or the like. A three-dimensional multi-axis fabric composite material is made by forming rods by bonding together bundles of fibers with a matrix, disposing a number of rods parallel to each other, orienting groups of rods along at least three axes, passing each rod in one group between rods of the other differently oriented groups, and bonding together adjoining rods with the matrix, etc.