  We report a detailed investigation of the elastic properties of Rb4LiH3(SO4)4
measured as a function of temperature and pressure. Rb4LiH3(SO4)4 is known to
show a 4 - 2 ferroelastic phase transition at Tc = 134 K. In order to clarify
the nature of the order parameter associated with that structural transition,
we compare our finding to two distinct phenomelogical Landau models. The
coupling parameters of both models are all determined using the temperature
dependence of the strain tensor, as well as the pressure dependence dTc/dP =
19.1 K/kbar, prior to the calculation of the elastic constants. Our comparison
indicates that the ferroelastic transition in Rb4LiH3(SO4)4 is fully consistent
(within a few percent) with the predictions of a pseudo-proper model, showing
at the same time that the primary mechanism leading to the phase transition is
not driven by strains. Our analysis also refutes the idea that Rb4LiH3(SO4)4 is
the first ferroelastic compound showing incomplete softening, of the effective
soft acoustic mode Csoft, at Tc.
