We have performed a Brillouin scattering study of methanol-water solutions at different molar fraction concentrations of methanol as a function of pressure. For that purpose a diamond anvil cell was used and pressures up to 25 kbar were reached. All measurements were carried out at ambient temperature. The data at P = 1 bar are in accordance with previous Brillouin scattering results, showing a maximum well defined in the elastic constants in the low concentrated solution (methanol poor) and afterwards a decrease for higher methanol concentrations. However, our pressure study for the different methanol concentrations reveals a change in this behavior at P similar to 4 kbar. The results indicate that the applied pressure induces a change in the elastic constants that could be followed in two well defined regimes: from ambient pressure up to 4 kbar and from this pressure to 10 kbar.