We investigate the phenomena of shape transition and shape coexistence in mesoscopic systems, specifically in atomic clusters and atomic nuclei. We focus particularly on the well-known shape transition in silicon clusters of n atoms, Si-n near n = 25, and the Samarium isotope chain near Sm-152. In both cases, we find that the shape transition region can be identified with a plateau in the curve of binding energy per particle vs. n(-1/3), where n is the number of particles. To underscore the similarity of this signature of shape evolution for diverse systems, we show that it also applies to the growth of Lennard-Jones clusters. (c) 2006 Elsevier B.V. All rights reserved.