Thin cylindrical shell structures can show interesting bistable behaviour. If made unstressed from isotropic materials they are only stable in the initial configuration, but if made from fibre-reinforced composites they may also have a second, stable configuration. If the layup of the composite is antisymmetric, this alternative stable configuration forms a tight coil; if the layup is symmetric the alternative stable configuration is helical. A simple two-parameter model for these structure is presented that is able to distinguish between these different behaviours.