We demonstrate that the equilibrium equations for an axisymmetric, nonlinear, anisotropic membrane under hydrostatic pressure allow explicit representation of the longitudinal and azimuthal stresses in terms of the associated longitudinal and azimuthal strains. We apply this result in a numerical simulation of the canine diaphragm. More precisely, we compute the deformation of the membrane under a quasi static increase in the intensity of the applied hydrostatic load. The associated strains are easily estimated via finite differences. As the membrane is inflated the set of achieved strains grows and as a result of our explicit representation formula, we recover larger and larger patches of the associated stress surfaces.