X-ray diffraction and ultrasonic measurements have been carried out simultaneously up to 7 GPa at ambient temperature on a polycrystalline sample of Fe64Ni36 Invar alloy. The bulk modulus is found to increase linearly with pressure with an unusual low value (1.4) of dB/dP up to about 3.1(2) GPa followed by a regular slope (3.6) at higher pressure. The observation of these two distinct regimes is in qualitative agreement with previous results on the variation of the iron magnetic moment, and can be interpreted using the 2gamma-state model in terms of gradual population of low spin-small volume state at the expense of the high spin-large volume state under pressure.