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We study the classical limit of the ELPR/FK spin foam models by analyzing thelarge-distance asymptotics of the corresponding graviton propagators. This isdone by examining the large-spin asymptotics of the Hartle-Hawking wavefunctionwhich is peaked around a classical flat spatial geometry. By using thestationary phase method we determine the wavefunction asymptotics. The obtainedasymptotics does not give the desired large-distance asymptotics for thecorresponding graviton propagator. However, we show that the ELPR/FK vertexamplitude can be redefined such that the corresponding Hartle-Hawkingwavefunction gives the desired asymptotics for the graviton propagator.

Graviton propagator asymptotics and the classical limit of ELPR/FK spin foam models