A composite material which has excellent ballistic performance and has improved flexibility. Surprisingly, it has been found that a combination of poly(alpha-olefin) fiber and matrix resin provides these desirable product features. The resin matrix is a block copolymer of a conjugated diene and a vinyl aromatic monomer, preferably a styrene-isoprene-styrene block copolymer, that is applied as an aqueous composition. The fiber has a tenacity of at least about 35 g/d and a tensile modulus of at least about 1200 g/d. The composite has a total density equal to or less than about 100 g/m2 and a stiffness of less than about 2.5 pounds (1.14 kg) for a two layer structure of the composite, and a total areal density equal to or less than about 190 g/m2 and a stiffness of less than about 3.0 pounds (1.36 kg) for a four layer structure of the composite. The Peel Strength for a two layer structure of less than about 1.0 pounds (0.45 kg) for a two layer structure of the composite, and less than about 0.7 pounds (0.32 kg) for a four layer structure of the composite. The process of this invention permits fabrication of these desirable products in a cost-effective manner. Body armor made from the composite has improved flexibility and excellent ballistic characteristics.