Injector for injecting fluid comprising - a valve comprising a valve body and a valve needle, - a solenoid actuator comprising an armature which is axially displaceable relative to the valve body and mechanically coupled to the valve needle so that it is operable to take the valve needle with it when it is displaced by means of a magnetic field which is generated by the solenoid when the actuator is energized for moving the valve needle away from a closing position, and - a damping element, wherein - the valve body extends between a fluid outlet end and a fluid inlet end along a central longitudinal axis and has a cavity, - the valve needle is arranged axially movable relative to the valve body in the cavity, is operable to seal the valve in the closing position, and is axially displaceable away from the closing position by the armature to unseal the valve, - the damping element is arranged within the cavity, and - the damping element comprises -- a hydraulic chamber, -- a piston being arranged axially movable relative to the valve body such that it is operable to modify a fluid volume of the hydraulic chamber and being coupled with the valve needle such that the piston reduces the fluid volume of the hydraulic chamber when the valve needle moves away from the closing position for unsealing the valve, and -- a flow restricting orifice hydraulically connecting the hydraulic chamber to the cavity, characterized in that the hydraulic chamber is positionally fix relative to the valve body. - a valve comprising a valve body and a valve needle, - a solenoid actuator comprising an armature which is axially displaceable relative to the valve body and mechanically coupled to the valve needle so that it is operable to take the valve needle with it when it is displaced by means of a magnetic field which is generated by the solenoid when the actuator is energized for moving the valve needle away from a closing position, and - a damping element, wherein - the valve body extends between a fluid outlet end and a fluid inlet end along a central longitudinal axis and has a cavity, - the valve needle is arranged axially movable relative to the valve body in the cavity, is operable to seal the valve in the closing position, and is axially displaceable away from the closing position by the armature to unseal the valve, - the damping element is arranged within the cavity, and - the damping element comprises -- a hydraulic chamber, -- a piston being arranged axially movable relative to the valve body such that it is operable to modify a fluid volume of the hydraulic chamber and being coupled with the valve needle such that the piston reduces the fluid volume of the hydraulic chamber when the valve needle moves away from the closing position for unsealing the valve, and -- a flow restricting orifice hydraulically connecting the hydraulic chamber to the cavity, characterized in that the hydraulic chamber is positionally fix relative to the valve body. -- a hydraulic chamber, -- a piston being arranged axially movable relative to the valve body such that it is operable to modify a fluid volume of the hydraulic chamber and being coupled with the valve needle such that the piston reduces the fluid volume of the hydraulic chamber when the valve needle moves away from the closing position for unsealing the valve, and -- a flow restricting orifice hydraulically connecting the hydraulic chamber to the cavity,