In an entanglement swapping process two initially uncorrelated qubits become entangled, without any direct interaction. We present a model using local variables aiming at reproducing this remarkable process, under the realistic assumption of finite detection efficiencies. The model assumes that the local variables describing the two qubits are initially completely uncorrelated. Nevertheless, we show that once conditioned on the Bell measurement result, the local variables bear enough correlation to simulate quantum measurement results with correlation very close to the quantum prediction. When only a partial Bell measurement is simulated, as carried out is all experiments so far, then the model recovers analytically the quantum prediction.