Bacterial flagella can adopt several different helical shapes in response to varying environmental conditions. A geometric model by Calladine ascribes these discrete shape changes to cooperative transitions between two stable tertiary structures of the constituent protein, flagellin, and predicts an ordered set of 12 helical states called polymorphic forms. Using long polymers of purified flagellin, we demonstrate controlled, reversible transformations between different polymorphic forms. While pulling on a single filament using an optical tweezer, we record the progressive transformation of the filament and also measure the force-extension curve. Both normal and coiled polymorphic forms stretch elastically with a bending stiffness of 3.5 pN x microm(2). At a force threshold of 4-7 pN or 3-5 pN (for normal and coiled forms, respectively), a fraction of the filament suddenly transforms to the next, longer, polymorphic form. This transformation is not deterministic because the force and amount of transformation vary from pull to pull. In addition, the force is highly dependent on stretching rate, suggesting that polymorphic transformation is associated with an activation energy.