A method is presented for the fast prediction of polymer crystal structures. From a stable helical conformation of the polymer chain well packed three dimensional periodic starting structures are generated using an adapted version of M. Blanco’s Molecular Silverware algorithm. These structures are then energy-minimised using classical molecular mechanics methods. The method only requires a rough estimate of the crystalline density. No information about crystal class, space group or cell parameters is necessary. Using this method, possible crystal structures of poly(ethylene ketone), Nylon-6,6 and poly(ethylene terephthalate) are calculated. Both the alpha- and beta-structures of poly(ethylene ketone) are correctly predicted. For Nylon-6,6 the lowest-energy structure obtained corresponds to the experimental alpha-structure. For poly(ethylene terephthalate) a large number of structures are generated using the algorithm. Besides the experimental structure four structures are found with a lower energy than the experimental structure.