This paper investigates the propagation of axisymmetric waves of finite deformation in polyisoprene rubber membranes subjected to high speed impact. High speed photography is used to monitor the motion and to determine the evolution of stretch and particle velocity in membranes at impact speeds of up to 160 m/s, producing a maximum stretch >8. A constitutive model is developed through a semi-inverse method correlating experimental results with simulations. The potential for formation of wrinkles is also addressed.