PURPOSE: To obtain a stabilized silane modified block copolymer by adding zinc oxide before melt kneading of a mixture of an unsatd. group-contg. alkoxysilane and a block copolymer comprising two kinds of blocks is ended.

CONSTITUTION: A mixture of 0.1-20 wt.%, preferably 0.5-10 wt.% of an unsatd. group-contg. alkoxysilane such as vinyltriethoxysilane, a block copolymer consisting of (A) monoalkenylarylene blocks such as styrene and (B) conjugated diene blocks such as butadiene and 0.01-3%, preferably 0.1-0.5%, of a radical initiator such as an org. peroxide is subjected to melt kneading in an extruder. Before the melt kneading step is ended, zinc oxide is added to the mixture in an amount of at least 0.15%, preferably 0.5-1.0%, to graft the silane on the block copolymer. An average molecular weight of A block in AB block is 3000-40000. A content of monoalkenylarene in AB block is preferably 10-30%.