The invention relates to a vibration isolator comprising a canister which ends are closed by end caps and a shaft able to move inside the canister, wherein the shaft comprises a piston-like shaped part for separating the canister in two parts: the first part being defined between the piston-like shaped part of the shaft and the first end cap, and comprising at least one resilient and damping element able to be compressed by a compression movement of the shaft on a first nominal stroke; the second part being defined between the piston-like shaped part of the shaft and the second end cap, and comprising at least one resilient and damping element able to be compressed by a tension movement of the shaft on a second nominal stroke; the tangential stiffness of the vibration isolator being, on at least one part of the first nominal stroke of the shaft, at least twice as lower as its tangential stiffness on the entire second nominal stroke of the shaft.