A method of suppressing the pogo effect on a vehicle having at least one reaction engine and a feed system for feeding said engine with at least one liquid propellant, said feed system being fitted with a hydraulic accumulator capable of selecting between a plurality of predetermined operating levels, each corresponding to a different volume of gas in the hydraulic accumulator, the method comprising the following steps: • calculating a current hydraulic resonant frequency for each mode of a set of hydraulic resonance modes of said feed system with a current level of said accumulator from among said predetermined levels; • calculating an alternative hydraulic resonant frequency for each mode of said set of hydraulic resonance modes of said feed system with each level of the predetermined levels that is an alternative to the current level; • calculating a current difference between each current hydraulic resonant frequency and a current mechanical resonant frequency for each mode of a set of mechanical resonance modes of a structure of said vehicle, and if a first reference criterion is not satisfied by all of the current differences: • calculating a set of differences between each alternative hydraulic resonant frequency and each current mechanical resonant frequency for each alternative level, and if said first reference criterion is satisfied by each set of differences of a plurality of alternative levels: • ordering the hydraulic accumulator to make a transition from the current level to an alternative level selected from among said alternative levels for which the first reference criterion is satisfied, and for which no hydraulic resonant frequency crosses any current mechanical resonant frequency during the transition. • calculating a current hydraulic resonant frequency for each mode of a set of hydraulic resonance modes of said feed system with a current level of said accumulator from among said predetermined levels; • calculating an alternative hydraulic resonant frequency for each mode of said set of hydraulic resonance modes of said feed system with each level of the predetermined levels that is an alternative to the current level; • calculating a current difference between each current hydraulic resonant frequency and a current mechanical resonant frequency for each mode of a set of mechanical resonance modes of a structure of said vehicle, and if a first reference criterion is not satisfied by all of the current differences: • calculating a set of differences between each alternative hydraulic resonant frequency and each current mechanical resonant frequency for each alternative level, and if said first reference criterion is satisfied by each set of differences of a plurality of alternative levels: • ordering the hydraulic accumulator to make a transition from the current level to an alternative level selected from among said alternative levels for which the first reference criterion is satisfied, and for which no hydraulic resonant frequency crosses any current mechanical resonant frequency during the transition. • ordering the hydraulic accumulator to make a transition from the current level to an alternative level selected from among said alternative levels for which the first reference criterion is satisfied, and for which no hydraulic resonant frequency crosses any current mechanical resonant frequency during the transition.