A shape-changing structure has a superelastic metal foam structural member that changes shape (morphs) to change configuration of the structure. The superelastic metal foam structural member changes shape while maintaining a continuous outer surface, with the continuous metal foam material inside the outer surface expanding, contracting, or otherwise changing shape. The superelastic metal foam material may be heated above a transition temperature to allow it to change shape, and then cooled to cause it to increase in strength, more easily maintaining its new shape. The superelastic metal foam material may be a suitable alloy, for example a nickel titanium alloy, that exhibits superelastic (pseudoelastic) behavior. The superelastic metal foam material may be a shape memory alloy material that returns to a set shape upon moderate heating. The superelastic metal elastic foam structural member may be heated either by an internal heat source or by external heating.