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This paper deals with the reconstruction of smooth, flexible, isometrically embedded flat surfaces in 3D, such as a sheet of paper or a flag waving in the wind, from a set of 2D projected observations such as camera images. To solve the problem, a set of matched features of the waving object at different poses is needed, which are then applied to the reconstruction algorithm here described. The complete algorithm consists of 2 phases, the first obtaining an initial approximation from local features, the second uses this result to iterate a global cost function, trying to achieve a better estimate. To validate the algorithm, synthetic data with noise is generated, reconstructed and compared to ground truth data. Also, a second experiment consisting of real images of a sheet of paper is shown.