A filling machine for filling containers with a pourable product, said filling machine comprising: - a product tank containing said pourable product and a gas maintained at a first pressure value (P 1); - at least one dosing tank filled with gas and adapted to measure out a given volume of pourable product to be fed to one container through first valve means; and - a fluidic line connecting said dosing tank to said product tank through second valve means; - first pressurizing means to selectively pressurize the gas in said dosing tank at a second pressure value (P 2), lower than said first pressure value (P 1), in a condition in which said first and second valve means (26, 28) are both in respective closed configurations and said dosing tank is product-free; characterized by further comprising: - sensor means to detect pressure of the gas in said dosing tank; and - control means configured: to set said second valve means in an open configuration after said dosing tank has been pressurized at said second pressure value (P 2), in order to allow said pourable product to flow from said product tank to said dosing tank under the action of the pressure difference therebetween; and to set said second valve means in said closed configuration as the gas pressure detected by said sensor means in said dosing tank, during flow of said pourable product into the dosing tank itself, reaches a third pressure value (P 4) correlated with said given volume of pourable product flowed in the dosing tank. - a product tank containing said pourable product and a gas maintained at a first pressure value (P 1); - at least one dosing tank filled with gas and adapted to measure out a given volume of pourable product to be fed to one container through first valve means; and - a fluidic line connecting said dosing tank to said product tank through second valve means; - first pressurizing means to selectively pressurize the gas in said dosing tank at a second pressure value (P 2), lower than said first pressure value (P 1), in a condition in which said first and second valve means (26, 28) are both in respective closed configurations and said dosing tank is product-free; - sensor means to detect pressure of the gas in said dosing tank; and - control means configured: to set said second valve means in an open configuration after said dosing tank has been pressurized at said second pressure value (P 2), in order to allow said pourable product to flow from said product tank to said dosing tank under the action of the pressure difference therebetween; and to set said second valve means in said closed configuration as the gas pressure detected by said sensor means in said dosing tank, during flow of said pourable product into the dosing tank itself, reaches a third pressure value (P 4) correlated with said given volume of pourable product flowed in the dosing tank. to set said second valve means in an open configuration after said dosing tank has been pressurized at said second pressure value (P 2), in order to allow said pourable product to flow from said product tank to said dosing tank under the action of the pressure difference therebetween; and to set said second valve means in said closed configuration as the gas pressure detected by said sensor means in said dosing tank, during flow of said pourable product into the dosing tank itself, reaches a third pressure value (P 4) correlated with said given volume of pourable product flowed in the dosing tank.