We introduce a numerical scheme to evolve functional elastic materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures, and the correlations among them can be computed. As an example, we consider an "allosteric" task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpetshaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies nonmonotonically along the trumpet. As previously shown for some proteins, we find that correlations appearing during evolution alone are sufficient to identify key aspects of this design. Finally, we show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials. Overall, our in silico evolution experiment offers a window to study the relationship between structure, function, and correlations emerging during evolution. disordered materials | proteins | evolution P roteins are long polymers that can fold in a reproducible way and achieve a specific function. Often, the activity of the main functional site depends on the binding of an effector on a distant site (1, 2). Such an allosteric behavior can occur over large distances, such as 20 residues or more (3), and often involves only a sparse subset of residues in the protein (3, 4). Allosteric regulation offers an appealing target for drug design (5), and there is considerable interest in predicting allosteric pathways (6, 7). One central difficulty is that the physical mechanisms allowing such an "action at a distance" remain elusive. In some cases, allostery can be understood as the modulation of a hinge connecting two extended rigid parts of the protein (8, 9), but, often, the displacement field induced by the binding of the effector cannot be described in these terms (4, 10, 11). Another route, statistical coupling analysis (12), considers correlations within sequences of proteins of the same family to infer allosteric pathways (4, 7). The generality of this elegant approach is, however, debated (13).From a physical viewpoint, specific response at a distance is surprising. The structure of proteins is similar to randomly packed spheres (14). Generically, the response of such systems is nonspecific and decays rapidly in space (in a manner similar to a continuum medium) at distances larger than the particle size; this is true, except close to a critical point where the number of constraints coming from strongly interacting particles is just sufficient to match the number of degrees of freedom of the particles (15). There, the elastic response becomes heterogeneous on all scales (16,17). This point is illustrated in Fig. 1A, showing the rapidly decaying response of a random spring network to a stimulus. However, as shown in Fig. 1B (and independently found in ref. 18 using a different algorithm), springs can be move...