The preservation of the wing membrane of pterosaurs is very poor and the available fossil evidence does not allow its properties to be reconstructed. In contrast, the fossil record for the wing bones is relatively good and the advent of CT scanning has made it possible to build high-fidelity structural models of the wing spar. The bending strength of the wing spar of a 6 m wingspan ornithocheirid pterosaur is used to infer the likely membrane tension. The tensions required to suppress aeroelastic flutter and to minimize ballooning of the membrane under flight loads are also estimated. All three estimates are of similar magnitude and imply that the membrane must have contained high-modulus material, supporting the view that the reinforcing aktinofibrils were keratinous.