The present invention generally relates to a woven preform for reinforced composite materials and a method of making thereof. Specifically, the present invention is a method of machine weaving fiber preforms for polymer matrix composites that consist of closed perimeters with multiple intersecting members in their interiors. More specifically, the invention is a woven preform and a method of forming thereof with closed cells at the outer edges with continuous hoop reinforcement in each cell of the preform. The woven preform is woven flat in both the warp and weft directions, and then unfolded to achieve the final shape of the structure, and can be processed into composite structural components using known methods such as resin transfer molding or chemical vapor infiltration. Thus, complicated shapes of all sizes can be woven on a conventional loom using the instant method.