The filled skutterudite compound SmRu4P12 undergoes a complex evolution from a paramagnetic metal (phase I) to a probable multipolar ordering insulator (phase II) at TMI ∼ 16.5 K, then to a magnetically ordered phase (phase III) at TN ∼ 14 K. Elastic properties under hydrostatic pressures were investigated to study the nature of the ordering phases. We found that distinct elastic softening above TMI 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 TMI under pressure. Strangely, the largest degree of softening is found in the transverse elastic constant CT at around 0.5-0.6 GPa, presumably having relevancy to the competing and very different Grüneisen parameters Ω of TMI and TN. Interplay between the two phase transitions is also verified by the rapid increase of TMI under pressure with a considerably large Ω of 9. Our results can be understood on the basis of the proposed octupole scenario for SmRu4P12.