An equilibrium phase diagram for the shape of compressively strained free-hanging films is developed by minimizing the total strain energy. For small strain gradients , the film wrinkles, while for sufficiently large , a phase transition from wrinkling to bending occurs. The average strain in the bilayer film is denoted . Thickness, Poisson's ratio, and the Young modulus for the first and second layers are denoted by , , and , , . The equilibrium radius of rolled-up tube is represented by and the wavelength of wrinkles by .