The authors study elastic behavior of a membrane, i.e. ``a material entity each possible configuration of which can be taken as some surface (i.e., a connected 2-dimensional submanifold with or without boundary) in \({\mathbb{R}}^ 3\)''. They rigorously show that a sphere cannot support residual stress, while a torus and a planar membrane can. They close by posing four unanswered questions, clearly challenging the readers much as one challenges students in a textbook. A clear and thorough treatment of interest to engineers with more than a passing familiarity with the mathematics of elasticity.