Thin membranes with curvature are investigated as mirror substrates for use in large optical telescopes. These films are mounted on an optically flat circular ring and stretched over a smaller optically flat circular ring where pressure or vacuum is applied to create the doubly curved surface as shown in figure 1. The films may vary in thickness from 20 to 200 microns. This particular experiment examines an aluminum coated 125 micron thick homogeneous, planar, isotropic membrane with a clear aperture of 28 centimeters. The nature of a flexible membrane implies that the surface curvature will result in an assorted array of gross surface figure issues associated with deterministic shape limits, probabilistic imperfections, nonlinear constitutive effects, and long-time- dependent effects. This report will focus on the empirical deterministic shape limits of a doubly curved membrane. Theoretical work on thin films inflated or evacuated into a doubly curved surface has a long history, and remains an active area of research. A number of articles [1,2,3,4,7] include summaries of this history, and offer insight on the deterministic membrane shapes.