Flow-induced vibration of small elastic cylinders mounted in the shear flow of a two-dimensional jet is investigated experimentally. There has been a great deal of work concerned with different vibrating conditions and practical dynamic responses by way of mass ratios and diameters of various different cylinders. In such cases, the amplitude of the cylinder oscillation changed along with the variation of the jet velocity is due to the influence of fluid elastic instability. The experiment is based on the method of the magnetic field induction to measure the motion of the small cylinder, and it involves measurements of the varying velocity in a jet through the hot- wire anemometer. The critical velocity of the cylinder vibration in the shear flow with different diameters, mass ratios and damping factors are examined. Moreover, the oscillation traces of the cylinder by fluid elastic instability were observed when the jet velocity was increased, and then decreased for examination of hysteresis phenomena. The results show that the bifurcation of the cylinder vibration traces is remarkable especially for cylinders with high mass ratios. By the amplitude diagrams of the cylinder vibration, the critical velocity for onset of fluid elastic vibration was determined. The dependence of the critical velocity and hysteresis phenomena on the mass ratio and damping factor are discussed.