The inflation of an isotropic, nonlinear elastic membrane by means of a volume independent hydrostatic pressure is studied. In particular, we consider annular membranes which, on the inner boundary, have been subjected to an axial twist and a displacement normal to the plane of the membrane, with the outer boundary fixed. A direct two-dimensional approach is adopted and by introducing a relaxed strain-energy function the occurrence of wrinkled solutions is considered. The governing equations are found to reduce to a system of first order differential equations, which are then solved numerically for a Mooney-Rivlin material, over a range of boundary value problems.