The present invention provides a rubber composition which when vulcanized may be used to form a safety support intended to be mounted on a wheel rim within a tire. The invention also is directed to such a support, capable of supporting a tread of the tire in the event of a drop in inflation pressure, and to a mounted assembly comprising this support. A rubber composition according to the invention comprises (phr: parts by weight per 100 parts of diene elastomer(s)): (a) a diene elastomer, (b) particles of an &agr;-olefinic thermoplastic polymer having a melting point greater than or equal to 150° C., in an amount of 5 to 30 parts by weight per 100 parts diene elastomer (phr), wherein the mean size by weight of the particles is between 50 &mgr;m and 500 &mgr;m, (c) greater than 60 phr of reinforcing filler, and (d) from 3 to 8 phr of sulphur.