Compliant multistable structures are presented which exhibit a large geometric change when actuated between their stable states. It is demonstrated how asymmetric-bistability is achieved through the combination of linear and nonlinear springs. Finite element analytical techniques are provided which enable the design of such structures, and which illustrate how the presence of imperfections can substantially alter their structural performance. A multistable structure is developed which consists of four connected bistable tetrahedral units. The validity of the analytical techniques is confirmed through observation of several physical models. (C) 2008 Elsevier Ltd. All rights reserved.