Helical structures, ubiquitous in nature, have inspired design and manufacturing of helical devices with applications in nanoelecromechanical systems, morphing structures, optoelectronics, microrobotics and drug delivery devices. Meanwhile, multi-stable structures have attracted increasing attention for their applications in bio-inspired robots and deployable aerospace components. Here we show that mechanical anisotropy and geometric nonlinearity can lead to novel selection principle of shape and multi-stability in helical ribbons, with table-top experiments performed to demonstrate the working principle. Our work will promote understanding of large deformation and instability of thin objects, and serve as a tool in developing functional structures for broad applications.