The large axisymmetric deformation of a plane circular membrane into surfaces of revolution by a lateral pressure is considered. The material is taken to be a styrene‐butadiene rubber for which a nonlinear integral type constitutive equation incorporating measured properties has been presented by McGuirt and Lianis [Trans. Soc. Rheol.,14, 117, (1970)]. The formulation is reduced to a two‐point boundary value problem governed by a system of nonlinear partial differential‐integral equations of Volterra type for principal stretch ratios and a related kinematic variable. A numerical procedure is outlined which reduces at each time step to solving a system of equations having the same general structure as that for the corresponding problem assuming the membrane to be elastic. Stretch ratio and stress variation and deformed profile histories are computed for prescribed pressure histories, the latter being most useful for comparison of predictions and experiment.