A process for producing a modified polymer rubber comprising the steps of:
(1) polymerizing a conjugated diene monomer or a combination thereof
with an aromatic vinyl monomer in a hydrocarbon solvent, in the presence
of an alkali metal catalyst or a specified alkali metal compound, to form
an alkali metal end-carrying active polymer, and (2) reacting the alkali
metal end-carrying active polymer with a specified isocyanurate compound
or a combination thereof with a specified coupling agent in a hydrocarbon
solvent.