The present invention relates to multidirectionally reinforced fiber preforms that conform easily to complex curvatures, such as, composite turbine fan cases, jet engine containment rings, aircraft fuselage frames, aircraft window frames, and flanged rings for attaching nacelles to aircraft engines. The present invention provides multidirectionally reinforced shape woven preforms with improved strength for composite structures that are axisymmetric as well as non-axisymmetric in nature. The invention is a preform used to reinforce a composite structure which includes a contour woven fabric portion, bi-axially braided, tri-axially braided or bias fabric portion, and/or a polar woven fabric portion, and a method of making thereof. The preform may optionally include a three-dimensionally woven portion. The combination of different forms of fabrics allows the preform to be produced without cutting and darting of the individual plies. Eliminating these cuts and darts improves the strength and performance of the resulting structure.