The object of the present invention is to provide an elastomer composite useful as the material for the plug of a medical vessel having excellent heat resistance, liquid leakage resistance, and a needle holding property, and the present invention provides an elastomer composite comprisinga block copolymer A derived from a polymer block Y1 containing a butadiene monomer unit as its main constitutional unit and two styrene polymer blocks, and a block copolymer P derived from a butadiene-styrene controlled distribution copolymer block Y2 and two polystyrene blocks X2, a softening agents having kinematic viscosity in the range of between 50 and 500 cSt, at 40°C, and a propylene polymer C having a modulus in bending in the range of between 1000 and 3000 MPa.
