The present invention relates to materials exhibiting the property of rubbery elasticity, consisting of molecules with a mass of between 9 and 9000 g/mol, all or some of the molecules having at least three groups (also referred to as “associative groups”) capable of associating via non-covalent interactions.Although consisting of small non-polymerized molecules that are not chemically crosslinked, this material exhibits properties of rubbery elasticity. According to an embodiment of the invention, this material exhibits rubbery elasticity at ambient temperature. Above a certain temperature, the material flows like a simple liquid. The material is thermoreversible, i.e. after cooling, the material again exhibits the property of rubbery elasticity. This material is self-repairing and potentially recyclable, which is never the case with a chemically crosslinked elastomer.According to an embodiment of the invention, the molecules constituting the material of the invention bear associative groups of formula (1) below: in which A denotes oxygen, sulphur or NH; the carbon atoms of formula (1) can be substituted. Preferably, A denotes oxygen. Advantageously, the material comprises (i) molecules having at least 3 associative groups, and (ii) molecules having a single associative group. Advantageously, the molecules are obtained from fatty acid derivatives.