This investigation proposes the use of the shadow moiré method (SMM) to measure stress in a thin film that is coated on a flexible substrate. The technique defines the profile of the sample by contour lines without the application of an external force, and the radius of curvature is calculated from these contour lines. The SMM is insensitive to environmental noise and has the same advantages as the interference method, such as being nondestructive and easy to use. For Al film with a thickness of 120 nm coated on a polyimide substrate by a DC magnetron sputtering system (800 W, room temperature), the stress is 0.45 +/- 0.042 GPa.