Provided are methods of forming composite structure over non-planar base structures and composite tools extending over cavities of the base structures. A tool may be formed from a composite layup cured on a flat mold. While applying the tool to the base structure, the tool may be bent around or about a bend axis. The bend axis may be parallel to continuous fibers within the tool. These fibers may span the full dimension of tool in the direction of the fibers. The continuous fibers extend across the cavity and provide stiffness to the tool in one direction even after bending of the tool. As such, the tool may withstand substantial forces in the direction perpendicular to its surface without collapsing into the cavity. In some embodiments, a composite structure may cured over the tool without impacting the size of the cavity on the other side of the tool.