The structural phase transition in two representatives of the rare earth elpasolite fluorides, Rb2NaHoF6 and Rb2NaTmF6, are studied in detail. The symmetry of the soft mode is determined from Raman spectra, X-ray and neutron powder diffraction data to be Γ4+. From the temperature dependence of the elastic constants of both compounds, estimates of various phase transition parameters are given, e.g. strain soft mode coupling constant and soft mode frequency. The softening of the elastic constants forT>Tc is explained by the strain coupling to the fluctuations of the soft mode coordinates. The energy of the soft phonon at the zone boundary is estimated from the data and compared with that of K2ReCl6. The phase transition mechanisms in rare earth elpasolites and hexahalometallates are discussed.