A recoil damper system (10) suitable for transmitting a dampened and reduced recoil to the user, comprising an insert (20) designed to be housed inside the stock (11) of a rifle (12), and intended to house damping means (40), a mobile interface (50) intended to inhibit the damping means (40), the mobile interface being fitted with sliding shafts (53) inside guides (23) provided in the insert (20), the mobile interface (50) is also made from plastic material suitable for deformation, when necessary, during the recoil in order to keep the rifle balanced, guaranteeing in the meantime the coaxial nature of the shafts (53) sliding inside the guides (23).