The effect of rigid particles on the fracture mode of polymers that yield with necking was analyzed theoretically with a model of regularly arrayed spherical particles. The adhesion between a polymer and particles was assumed to be weak, and particles were assumed to debond from the polymer before necking. A linear decrease in engineering draw stress with an increase in the filler content was derived. An increase in filler content leads to a transition in deformation mechanism. The transition depends on the ability of the polymer to strain-harden. If the ability to strain-harden is insignificant and the engineering fracture stress (strength) of the polymer is lower than its yield stress, the transition is from ductile to brittle fracture. If the ability to strain-harden is essential and the strength of the unfilled polymer is higher than its yield stress, the transition (ductile-to-ductile) is from neck propagation to uniform ductile yield. The critical filler contents were determined for both transitions from the properties of an unfilled polymer. The ductile-to-ductile transition without embrittlement is possible if the strength of the unfilled polymer is higher than its yield stress. Results for polymers filled by weakly bonded particles were compared with polymers filled by particles that debond after the yield stress.