The invention concerns a device comprising elastic stress-absorbing means for installed between first (10) and second (11) rigid annular members centered on the launch vehicle longitudinal axis and integral with the launch vehicle (1) and the payload (4) respectively, and device for controlling the elastic stress-absorbing devices capable of adapting the device rigidity to the different phases of the launching vehicle flight. The invention is characterized in that the control device comprise at least a plurality of hydraulic stops (13j) each arranged between the first (10) and second (11) rigid annular members, the stops (13j) being mobile at least between a first position wherein the rigidly link the annular members (10, 11) and a second position wherein the elastic stress-absorbing devices are activated.