Plants such as Dionaea muscipula (Venus Flytrap) can change the shape of their shell-like leaves by actively altering the cell pressures. These leaves are hydraulic actuators that do not require any complex controls and that possess an energy efficiency that is unmatched by natural or artificial muscles (Huber et al 1997 Proc. R. Soc. A 453 2185-205). We extend our previous work (Pagitz et al 2012 Bioinspir. Biomim. 7 016007) on pressure-actuated cellular structures by introducing a concept for shape-changing shell-like structures that can significantly alter their Gaussian curvature. The potential of this concept is demonstrated by a hemispherical shell that can reversibly change the sign of its Gaussian curvature. Furthermore, it is shown that a snap-through behaviour, similar to the one known from Dionaea muscipula, can be achieved by lowering the pressure in a single layer of cells.