  The filled skutterudite compound SmRu_4P_{12} undergoes a complex evolution
from a paramagnetic metal (phase I) to a probable multipolar ordering insulator
(phase II) at T_{MI} = 16.5 K, then to a magnetically ordered phase (phase III)
at T_{N} = 14 K. Elastic properties under hydrostatic pressures were
investigated to study the nature of the ordering phases. We found that distinct
elastic softening above T_{MI} is induced by pressure, giving evidence of
quadrupole degeneracy of the ground state in the crystalline electric field. It
also suggests that quadrupole moment may be one of the order parameters below
T_{MI} under pressure. Strangely, the largest degree of softening is found in
the transverse elastic constant C_{T} at around 0.5-0.6 GPa, presumably having
relevancy to the competing and very different Gruneisen parameters \Omega of
T_{MI} and T_{N}. Interplay between the two phase transitions is also verified
by the rapid increase of T_{MI} under pressure with a considerably large \Omega
of 9. Our results can be understood on the basis of the proposed octupole
scenario for SmRu_4P_{12}.
