This invention is based upon the discovery that a polydiene rubber that is comprised of repeat units that are derived from a conjugated diene monomer and sulfur can be used to improved the force ductility, elastic recovery, toughness and tenacity of asphalt cement. The polydiene rubber that is comprised of repeat units that are derived from a conjugated diene monomer and sulfur also exhibits excellent compatibility with asphalt. The repeat units in the polydiene rubber that are derived from sulfur are in the backbone of the polymer. These repeat units that are derived from sulfur typically contain from 2 to 8 sulfur atoms (--S.sub.n --). The subject invention more specifically relates to a modified asphalt cement which is comprised of (i) from about 90 weight percent to about 99 weight percent asphalt; (ii) from about 1 weight percent to about 10 weight percent of a polydiene rubber that is comprised of repeat units that are derived from a conjugated diene monomer and sulfur. The present invention also reveals an asphalt concrete which is comprised of (A) from about 90 weight percent to about 99 weight percent of an aggregate and (B) from about 1 weight percent to about 10 weight percent of a modified asphalt cement which is comprised of (i) from about 90 weight percent to about 99 weight percent asphalt; (ii) from about 1 weight percent to about 10 weight percent of a polydiene rubber that is comprised of repeat units that are derived from a conjugated diene monomer and sulfur. The present invention also discloses a process for preparing a modified asphalt cement which comprises (1) blending from about 1 to about 10 parts by weight of a polydiene rubber that is comprised of repeat units that are derived from a conjugated diene monomer and sulfur into from about 90 to about 99 parts by weight of asphalt at a temperature which is within the range of about 130.degree. to about 230.degree. C. to produce a polymer-asphalt blend; and (2) mixing from about 0.1 to about 3 parts by weight of sulfur into the polymer-asphalt blend to produce the modified asphalt cement.