The invention relates to a shock absorber for an aircraft undercarriage, the shock absorber comprising a main cylinder in which a rod is mounted to slide telescopically, the shock absorber having one or more pneumatic chambers filled with gas, a supply of hydraulic fluid, and throttle means for throttling the hydraulic fluid such that when the shock absorber is shortened, the gas in the pneumatic chamber(s) is compressed and the hydraulic fluid is throttled, in which the pneumatic chamber(s) is/are fully contained in one or more auxiliary cylinders external to the main cylinder, and in each of which a sealed piston is slidably mounted to separate a pneumatic chamber contained in said external auxiliary cylinder from a fluid chamber in fluid flow communication with the main cylinder. According to the invention, the throttle means are disposed at the inlet of a fluid flow connection between the main cylinder and the auxiliary cylinder(s).