This paper presents a three-dimensional finite element method for comp
uting stress and deformation of membrane structures. A conjugate pair
of strain and stress tensors, the Green strain tensor and the Second P
iola-Kirchhoff stress tensor are adopted to give the constitutive equa
tion of Mooney material. By means of exploiting the plane stress condi
tion of membrane, the hydrostatic pressure is directly expressed as fu
nctions of strains. Complex membrane structures, like those initially
in box shape with abrupt changes in geometry, can also be analyzed by
the proposed method.