Composites based on various polymers and rubber particles as a filler were studied. As the filler concentration was increased, the transition from necking to brittle fracture and then to uniform ductile yielding was observed. The criterion for the brittle-ductile transition, which is accompanied by an increase in the elongation at break, is equality between the tensile strength and the upper yield stress of the filled composite. Upon the brittle-ductile transition, the critical concentration of rubber particles is determined by two parameters: the height of the yield drop (difference between the upper and lower yield stresses of matrix polymer) and adhesive strength at the interface between the matrix polymer and filler particles (in the case of good adhesion, tensile strength of rubber particles). The larger the yield drop, the broader the concentration range corresponding to the polymer brittle fracture. The enhancement of adhesion between the matrix and the particles makes it possible to displace the brittle-ductile transition to lower filler contents and, hence, to narrow the region of brittle fracture of the composite.