The organopolysiloxane compositions comprising (a) a linear diorganopolysiloxane having a block structure composed of alternately linked two kinds of blocks of dimethylsiloxane units on one hand and of dimethylsiloxane units and methylvinylsiloxane units on the other hand, (b) a silica filler, (c) a methylhydrogenpolysiloxane as a crosslinking agent, and (d) a platinum catalyst for accelerating crosslinking by addition reaction. Cured silicone rubber elastomers obtained from the composition have very excellent mechanical properties, especially tear strength.